R12alphabeta[x_]=(a0+a1 x+a2 x^2+a3 x^3+a4 x^4+a5 x^5+a6 x^6+a7 x^7+a8 x^8+a9 x^9+a10 x^10-12 s x^11+x^12)/.a0->1/45875200 (-782757789696 s^10+1467670855680 s^9 (\[Alpha]+\[Beta])-163074539520 s^8 (-2+6 \[Alpha]^2+17 \[Alpha] \[Beta]+6 \[Beta]^2)+10192158720 s^7 (-42 \[Alpha]+19 \[Alpha]^3-42 \[Beta]+191 \[Alpha]^2 \[Beta]+191 \[Alpha] \[Beta]^2+19 \[Beta]^3)+49545216 s^6 (-928+1575 \[Alpha]^4-10860 \[Alpha]^3 \[Beta]+3336 \[Beta]^2+1575 \[Beta]^4+\[Alpha]^2 (3336-29638 \[Beta]^2)-4 \[Alpha] \[Beta] (-2996+2715 \[Beta]^2))-6193152 s^5 (7707 \[Alpha]^5+3775 \[Alpha]^4 \[Beta]-2 \[Alpha]^3 (668+39941 \[Beta]^2)+\[Alpha]^2 (44056 \[Beta]-79882 \[Beta]^3)+\[Alpha] (-5760+44056 \[Beta]^2+3775 \[Beta]^4)+\[Beta] (-5760-1336 \[Beta]^2+7707 \[Beta]^4))+20480 s^4 (86272+397467 \[Alpha]^6+2316762 \[Alpha]^5 \[Beta]-210960 \[Beta]^2-970704 \[Beta]^4+397467 \[Beta]^6-63 \[Alpha]^4 (15408+38821 \[Beta]^2)+\[Alpha]^3 (1500192 \[Beta]-9800116 \[Beta]^3)+6 \[Alpha] \[Beta] (-275888+250032 \[Beta]^2+386127 \[Beta]^4)-3 \[Alpha]^2 (70320-2450848 \[Beta]^2+815241 \[Beta]^4))-30720 s^3 (27 \[Alpha]^7+318864 \[Alpha]^6 \[Beta]+7 \[Alpha]^5 (-19659+56162 \[Beta]^2)-5 \[Alpha]^4 \[Beta] (69437+225797 \[Beta]^2)+\[Alpha]^3 (80120+999166 \[Beta]^2-1128985 \[Beta]^4)+\[Alpha]^2 (-276296 \[Beta]+999166 \[Beta]^3+393134 \[Beta]^5)+\[Beta] (21488+80120 \[Beta]^2-137613 \[Beta]^4+27 \[Beta]^6)+\[Alpha] (21488-276296 \[Beta]^2-347185 \[Beta]^4+318864 \[Beta]^6))-(\[Alpha]-\[Beta])^2 (-403200+176769 \[Alpha]^8+3296088 \[Alpha]^7 \[Beta]+1478400 \[Beta]^2+1262816 \[Beta]^4-1844304 \[Beta]^6+176769 \[Beta]^8+84 \[Alpha]^6 (-21956+52251 \[Beta]^2)-24 \[Alpha]^5 \[Beta] (185996+778257 \[Beta]^2)+\[Alpha]^4 (1262816+25256784 \[Beta]^2-40299066 \[Beta]^4)-8 \[Alpha]^3 \[Beta] (1358000-7305096 \[Beta]^2+2334771 \[Beta]^4)+8 \[Alpha] \[Beta] (705600-1358000 \[Beta]^2-557988 \[Beta]^4+412011 \[Beta]^6)+4 \[Alpha]^2 (369600-7385008 \[Beta]^2+6314196 \[Beta]^4+1097271 \[Beta]^6))-32 s^2 (4412745 \[Alpha]^8-17086320 \[Alpha]^7 \[Beta]+1680 \[Alpha]^5 \[Beta] (56749+16323 \[Beta]^2)-420 \[Alpha]^6 (-11934+257357 \[Beta]^2)+16 \[Alpha]^3 \[Beta] (-361944-16966538 \[Beta]^2+1713915 \[Beta]^4)+2 \[Alpha]^4 (-10272384-5643036 \[Beta]^2+122541259 \[Beta]^4)-16 \[Alpha] \[Beta] (834928+361944 \[Beta]^2-5958645 \[Beta]^4+1067895 \[Beta]^6)-4 \[Alpha]^2 (-449952-25665088 \[Beta]^2+2821518 \[Beta]^4+27022485 \[Beta]^6)+3 (251136+599936 \[Beta]^2-6848256 \[Beta]^4+1670760 \[Beta]^6+1470915 \[Beta]^8))+4 s (3041475 \[Alpha]^9+403200 \[Beta]+8524395 \[Alpha]^8 \[Beta]+7967232 \[Beta]^3-8198688 \[Beta]^5-7450752 \[Beta]^7+3041475 \[Beta]^9-12 \[Alpha]^7 (620896+5200907 \[Beta]^2)+\[Alpha]^6 (50938752 \[Beta]-90084500 \[Beta]^3)+2 \[Alpha]^4 \[Beta] (-29160656-91348416 \[Beta]^2+73905397 \[Beta]^4)+2 \[Alpha]^5 (-4099344+62723136 \[Beta]^2+73905397 \[Beta]^4)+\[Alpha]^3 (7967232+76268480 \[Beta]^2-182696832 \[Beta]^4-90084500 \[Beta]^6)-4 \[Alpha]^2 \[Beta] (2708608-19067120 \[Beta]^2-31361568 \[Beta]^4+15602721 \[Beta]^6)+\[Alpha] (403200-10834432 \[Beta]^2-58321312 \[Beta]^4+50938752 \[Beta]^6+8524395 \[Beta]^8)))/.a1->1/137625600 (-2336247 \[Alpha]^11-2348273369088 s^10 (1+\[Alpha])-3 \[Alpha]^10 (778749+120310 \[Beta])-3 \[Alpha]^9 (-954384+120310 \[Beta]+1554237 \[Beta]^2)+\[Alpha]^8 (4433712+5998848 \[Beta]-4662711 \[Beta]^2-105301816 \[Beta]^3)-2 \[Alpha]^7 (-366576-9667584 \[Beta]-99541248 \[Beta]^2+52650908 \[Beta]^3+102409111 \[Beta]^4)-2 \[Alpha]^6 (5047824+52664352 \[Beta]-82437888 \[Beta]^2-207023296 \[Beta]^3+102409111 \[Beta]^4+18641014 \[Beta]^5)+2 \[Alpha]^5 (6212480-41443872 \[Beta]-166652976 \[Beta]^2+164596416 \[Beta]^3-19720528 \[Beta]^4-18641014 \[Beta]^5+77456749 \[Beta]^6)+2 \[Alpha]^4 (6919040+61120000 \[Beta]-96557616 \[Beta]^2+50658624 \[Beta]^3+32356272 \[Beta]^4-164105344 \[Beta]^5+77456749 \[Beta]^6+42265092 \[Beta]^7)-\[Beta]^2 (-1209600+12369920 \[Beta]+4435200 \[Beta]^2+1413120 \[Beta]^3+3788448 \[Beta]^4-10828800 \[Beta]^5-5532912 \[Beta]^6+1570560 \[Beta]^7+530307 \[Beta]^8)-\[Alpha]^3 (15998720-46238720 \[Beta]+58186240 \[Beta]^2+50485632 \[Beta]^3-264184608 \[Beta]^4+224057088 \[Beta]^5+17075584 \[Beta]^6-84530184 \[Beta]^7+11378811 \[Beta]^8)-\[Alpha] \[Beta] (2419200-13579520 \[Beta]+20433920 \[Beta]^2-71566080 \[Beta]^3-38755776 \[Beta]^4+26229408 \[Beta]^5-13154688 \[Beta]^6+7803408 \[Beta]^7+10398210 \[Beta]^8+530307 \[Beta]^9)-\[Alpha]^2 (3628800-9950720 \[Beta]-16401920 \[Beta]^2+95022080 \[Beta]^3-112381728 \[Beta]^4+101434944 \[Beta]^5+101929344 \[Beta]^6-47361408 \[Beta]^7+11378811 \[Beta]^8+10398210 \[Beta]^9)+489223618560 s^9 (4+13 \[Alpha]^2+9 \[Beta]+\[Alpha] (13+9 \[Beta]))-489223618560 s^8 (-2+15 \[Alpha]^3+6 \[Beta]+6 \[Beta]^2+\[Alpha]^2 (15+23 \[Beta])+\[Alpha] (4+23 \[Beta]+6 \[Beta]^2))+10192158720 s^7 (-80+459 \[Alpha]^4-126 \[Beta]+138 \[Beta]^2+57 \[Beta]^3+\[Alpha]^3 (459+1193 \[Beta])+\[Alpha]^2 (-68+1193 \[Beta]+711 \[Beta]^2)+\[Alpha] (-206+326 \[Beta]+711 \[Beta]^2+57 \[Beta]^3))-148635648 s^6 (928+11985 \[Alpha]^5-5280 \[Beta]-3336 \[Beta]^2+360 \[Beta]^3-1575 \[Beta]^4+15 \[Alpha]^4 (799+3228 \[Beta])+2 \[Alpha]^3 (-6048+24210 \[Beta]+25079 \[Beta]^2)+2 \[Alpha]^2 (-6228-172 \[Beta]+25079 \[Beta]^2+5610 \[Beta]^3)+\[Alpha] (-4352-17264 \[Beta]+13584 \[Beta]^2+11220 \[Beta]^3-1575 \[Beta]^4))+6193152 s^5 (16640+65619 \[Alpha]^6+17280 \[Beta]-26880 \[Beta]^2+4008 \[Beta]^3-25740 \[Beta]^4-23121 \[Beta]^5+207 \[Alpha]^5 (317+1965 \[Beta])+23 \[Alpha]^4 (-7164+17685 \[Beta]+29002 \[Beta]^2)+2 \[Alpha]^3 (-69516-133724 \[Beta]+333523 \[Beta]^2+147663 \[Beta]^3)+\[Alpha]^2 (7040-335368 \[Beta]+98672 \[Beta]^2+295326 \[Beta]^3-37065 \[Beta]^4)-\[Alpha] (-33920+123520 \[Beta]+159048 \[Beta]^2-71928 \[Beta]^3+37065 \[Beta]^4+23121 \[Beta]^5))-61440 s^4 (-86272+848421 \[Alpha]^7+838656 \[Beta]+210960 \[Beta]^2+804384 \[Beta]^3+970704 \[Beta]^4-772632 \[Beta]^5-397467 \[Beta]^6+63 \[Alpha]^6 (13467+134866 \[Beta])+63 \[Alpha]^5 (-70360+134866 \[Beta]+342693 \[Beta]^2)+\[Alpha]^4 (-3660048-15685272 \[Beta]+21589659 \[Beta]^2+16504324 \[Beta]^3)+\[Alpha]^3 (2837808-14150592 \[Beta]-5793168 \[Beta]^2+16504324 \[Beta]^3-215397 \[Beta]^4)-3 \[Alpha]^2 (-677808+708224 \[Beta]+4135552 \[Beta]^2-1972560 \[Beta]^3+71799 \[Beta]^4+1029798 \[Beta]^5)-\[Alpha] (-752384-2493984 \[Beta]+4407696 \[Beta]^2+695808 \[Beta]^3+563976 \[Beta]^4+3089394 \[Beta]^5+397467 \[Beta]^6))+10240 s^3 (-350720+318600 \[Alpha]^8-193392 \[Beta]-92304 \[Beta]^2-721080 \[Beta]^3+2193912 \[Beta]^4+1238517 \[Beta]^5-309393 \[Beta]^6-243 \[Beta]^7+54 \[Alpha]^7 (5900+107989 \[Beta])+189 \[Alpha]^6 (-18372+30854 \[Beta]+126935 \[Beta]^2)+7 \[Alpha]^5 (-451845-3371571 \[Beta]+3427245 \[Beta]^2+4288595 \[Beta]^3)+\[Alpha]^4 (5751216-19378359 \[Beta]-27027645 \[Beta]^2+30020165 \[Beta]^3+5604894 \[Beta]^4)+\[Alpha]^3 (3557304+7493928 \[Beta]-28478094 \[Beta]^2+6869150 \[Beta]^3+5604894 \[Beta]^4-8765568 \[Beta]^5)-\[Alpha]^2 (636416-8001384 \[Beta]+10401144 \[Beta]^2+6853950 \[Beta]^3-6769026 \[Beta]^4+8765568 \[Beta]^5+3179169 \[Beta]^6)-\[Alpha] (544112-3595632 \[Beta]-2394360 \[Beta]^2+1228536 \[Beta]^3-5318577 \[Beta]^4+2984121 \[Beta]^5+3179169 \[Beta]^6+243 \[Beta]^7))-96 s^2 (1596465 \[Alpha]^9+15 \[Alpha]^8 (106431+2106952 \[Beta])+20 \[Alpha]^7 (-982452+1580214 \[Beta]+12614777 \[Beta]^2)+20 \[Alpha]^6 (-1247106-14741770 \[Beta]+12614777 \[Beta]^2+26185702 \[Beta]^3)+\[Alpha]^5 (76641952-246747920 \[Beta]-700601952 \[Beta]^2+523714040 \[Beta]^3+258966478 \[Beta]^4)-2 \[Alpha]^4 (-27876416-162314448 \[Beta]+297735036 \[Beta]^2+74436524 \[Beta]^3-129483239 \[Beta]^4+90566700 \[Beta]^5)-4 \[Alpha]^3 (13408448-52414464 \[Beta]+11408272 \[Beta]^2+81992472 \[Beta]^3-84165692 \[Beta]^4+45283350 \[Beta]^5+38531535 \[Beta]^6)-4 \[Alpha]^2 (5213408-10472608 \[Beta]-35361888 \[Beta]^2+56412976 \[Beta]^3-39391482 \[Beta]^4-2773890 \[Beta]^5+38531535 \[Beta]^6+2948310 \[Beta]^7)+3 (251136-2117120 \[Beta]+599936 \[Beta]^2-10926720 \[Beta]^3-6848256 \[Beta]^4+6963040 \[Beta]^5+1670760 \[Beta]^6+1764360 \[Beta]^7+1470915 \[Beta]^8)+\[Alpha] (-5597952-19710208 \[Beta]+63400448 \[Beta]^2-38571264 \[Beta]^3+94426272 \[Beta]^4+116227440 \[Beta]^5-43075200 \[Beta]^6-11793240 \[Beta]^7+4412745 \[Beta]^8))+4 s (6968320+7014285 \[Alpha]^10+1209600 \[Beta]+28830720 \[Beta]^2+23901696 \[Beta]^3-78879360 \[Beta]^4-24596064 \[Beta]^5-21940800 \[Beta]^6-22352256 \[Beta]^7+17657460 \[Beta]^8+9124425 \[Beta]^9+15 \[Alpha]^9 (467619+393823 \[Beta])+3 \[Alpha]^8 (-2232452+1969115 \[Beta]+83327996 \[Beta]^2)+12 \[Alpha]^7 (-2029568-26428872 \[Beta]+20831999 \[Beta]^2+82528775 \[Beta]^3)+2 \[Alpha]^6 (35044848-157759392 \[Beta]-827396232 \[Beta]^2+495172650 \[Beta]^3+488165171 \[Beta]^4)-2 \[Alpha]^5 (-46015248-447144912 \[Beta]+657893472 \[Beta]^2+703346288 \[Beta]^3-488165171 \[Beta]^4+122386089 \[Beta]^5)-2 \[Alpha]^4 (75412032-276375312 \[Beta]-415174080 \[Beta]^2+696059648 \[Beta]^3-486886172 \[Beta]^4+122386089 \[Beta]^5+334211790 \[Beta]^6)-4 \[Alpha]^3 (17986176+62354944 \[Beta]-177967440 \[Beta]^2+257602480 \[Beta]^3-63199776 \[Beta]^4-180649464 \[Beta]^5+167105895 \[Beta]^6+39859383 \[Beta]^7)+\[Alpha]^2 (37008640-135870976 \[Beta]+452945664 \[Beta]^2-59229120 \[Beta]^3-135364896 \[Beta]^4+737171136 \[Beta]^5-208130064 \[Beta]^6-159437532 \[Beta]^7+43230645 \[Beta]^8)+\[Alpha] (8177920-81191680 \[Beta]-3672576 \[Beta]^2-89647104 \[Beta]^3-253843296 \[Beta]^4+316943136 \[Beta]^5+130875456 \[Beta]^6-23979936 \[Beta]^7+43230645 \[Beta]^8+9124425 \[Beta]^9)))/.a2->1/45875200 (782757789696 s^10-1467670855680 s^9 (\[Alpha]+\[Beta])+163074539520 s^8 (-5+6 \[Alpha]^2+17 \[Alpha] \[Beta]+6 \[Beta]^2)-10192158720 s^7 (-98 \[Alpha]+19 \[Alpha]^3-98 \[Beta]+191 \[Alpha]^2 \[Beta]+191 \[Alpha] \[Beta]^2+19 \[Beta]^3)-49545216 s^6 (-4768+1575 \[Alpha]^4-10860 \[Alpha]^3 \[Beta]+6936 \[Beta]^2+1575 \[Beta]^4+\[Alpha]^2 (6936-29638 \[Beta]^2)-4 \[Alpha] \[Beta] (-6716+2715 \[Beta]^2))+6193152 s^5 (7707 \[Alpha]^5+3775 \[Alpha]^4 \[Beta]-2 \[Alpha]^3 (2708+39941 \[Beta]^2)+\[Alpha]^2 (92936 \[Beta]-79882 \[Beta]^3)+\[Alpha] (-26560+92936 \[Beta]^2+3775 \[Beta]^4)+\[Beta] (-26560-5416 \[Beta]^2+7707 \[Beta]^4))-20480 s^4 (1070080+397467 \[Alpha]^6+2316762 \[Alpha]^5 \[Beta]-646416 \[Beta]^2-2097144 \[Beta]^4+397467 \[Beta]^6-63 \[Alpha]^4 (33288+38821 \[Beta]^2)+\[Alpha]^3 (2558592 \[Beta]-9800116 \[Beta]^3)+6 \[Alpha] \[Beta] (-1211312+426432 \[Beta]^2+386127 \[Beta]^4)-3 \[Alpha]^2 (215472-5095504 \[Beta]^2+815241 \[Beta]^4))+30720 s^3 (27 \[Alpha]^7+318864 \[Alpha]^6 \[Beta]-65 \[Alpha]^4 \[Beta] (12197+17369 \[Beta]^2)+7 \[Alpha]^5 (-35607+56162 \[Beta]^2)+\[Alpha]^3 (374120+1976646 \[Beta]^2-1128985 \[Beta]^4)+2 \[Alpha]^2 \[Beta] (-547452+988323 \[Beta]^2+196567 \[Beta]^4)+\[Beta] (213232+374120 \[Beta]^2-249249 \[Beta]^4+27 \[Beta]^6)+\[Alpha] (213232-1094904 \[Beta]^2-792805 \[Beta]^4+318864 \[Beta]^6))+32 s^2 (17055488+4412745 \[Alpha]^8-17086320 \[Alpha]^7 \[Beta]+24613248 \[Beta]^2-74425728 \[Beta]^4+2961000 \[Beta]^6+4412745 \[Beta]^8+5040 \[Alpha]^5 \[Beta] (37101+5441 \[Beta]^2)-420 \[Alpha]^6 (-7050+257357 \[Beta]^2)+16 \[Alpha]^3 \[Beta] (-2985624-33881438 \[Beta]^2+1713915 \[Beta]^4)+\[Alpha]^4 (-74425728+979608 \[Beta]^2+245082518 \[Beta]^4)-16 \[Alpha] \[Beta] (7923728+2985624 \[Beta]^2-11686815 \[Beta]^4+1067895 \[Beta]^6)-12 \[Alpha]^2 (-2051104-33995136 \[Beta]^2-81634 \[Beta]^4+9007495 \[Beta]^6))+3 (-537600+58923 \[Alpha]^10+980850 \[Alpha]^9 \[Beta]-2464000 \[Beta]^2+2352000 \[Beta]^4+2368992 \[Beta]^6-1072708 \[Beta]^8+58923 \[Beta]^10-696 \[Alpha]^7 \[Beta] (2452+11571 \[Beta]^2)-13 \[Alpha]^8 (82516+51957 \[Beta]^2)+\[Alpha]^6 (2368992+20133776 \[Beta]^2+482118 \[Beta]^4)+4 \[Alpha]^5 \[Beta] (-3586896+1042648 \[Beta]^2+3603483 \[Beta]^4)+8 \[Alpha]^3 \[Beta] (1108800+5804496 \[Beta]^2+521324 \[Beta]^4-1006677 \[Beta]^6)+2 \[Alpha]^4 (1176000-5619696 \[Beta]^2-21525068 \[Beta]^4+241059 \[Beta]^6)+2 \[Alpha] \[Beta] (2464000+4435200 \[Beta]^2-7173792 \[Beta]^4-853296 \[Beta]^6+490425 \[Beta]^8)-\[Alpha]^2 (2464000+22444800 \[Beta]^2+11239392 \[Beta]^4-20133776 \[Beta]^6+675441 \[Beta]^8))-4 s (3041475 \[Alpha]^9+8524395 \[Alpha]^8 \[Beta]-12 \[Alpha]^7 (1438196+5200907 \[Beta]^2)+\[Alpha]^6 (82326192 \[Beta]-90084500 \[Beta]^3)+2 \[Alpha]^4 \[Beta] (-116768496-174627816 \[Beta]^2+73905397 \[Beta]^4)+2 \[Alpha]^5 (-7314864+130911816 \[Beta]^2+73905397 \[Beta]^4)-4 \[Alpha]^2 \[Beta] (21101888-69138000 \[Beta]^2-65455908 \[Beta]^4+15602721 \[Beta]^6)-4 \[Alpha]^3 (-16532288-69138000 \[Beta]^2+87313908 \[Beta]^4+22521125 \[Beta]^6)+\[Beta] (7392000+66129152 \[Beta]^2-14629728 \[Beta]^4-17258352 \[Beta]^6+3041475 \[Beta]^8)+\[Alpha] (7392000-84407552 \[Beta]^2-233536992 \[Beta]^4+82326192 \[Beta]^6+8524395 \[Beta]^8)))/.a3->-((497664 s^9)/35)+746496/35 s^8 (\[Alpha]+\[Beta])-5184/35 s^7 (-88+69 \[Alpha]^2+226 \[Alpha] \[Beta]+69 \[Beta]^2)+648/5 s^6 (-92 \[Alpha]+3 \[Alpha]^3-92 \[Beta]+141 \[Alpha]^2 \[Beta]+141 \[Alpha] \[Beta]^2+3 \[Beta]^3)+9/10 s^5 (-3520+1287 \[Alpha]^4-3396 \[Alpha]^3 \[Beta]+2496 \[Beta]^2+1287 \[Beta]^4+\[Alpha]^2 (2496-12886 \[Beta]^2)-4 \[Alpha] \[Beta] (-3584+849 \[Beta]^2))-9/40 s^4 (1533 \[Alpha]^5+3045 \[Alpha]^4 \[Beta]-6 \[Alpha]^3 (586+2187 \[Beta]^2)-2 \[Alpha]^2 \[Beta] (-8902+6561 \[Beta]^2)+\[Beta] (-6464-3516 \[Beta]^2+1533 \[Beta]^4)+\[Alpha] (-6464+17804 \[Beta]^2+3045 \[Beta]^4))+1/13440 s^3 (2995712+309393 \[Alpha]^6+4222638 \[Alpha]^5 \[Beta]+769680 \[Beta]^2-4189752 \[Beta]^4+309393 \[Beta]^6-63 \[Alpha]^4 (66504+23023 \[Beta]^2)-4 \[Alpha]^3 \[Beta] (-66384+3430775 \[Beta]^2)+\[Alpha]^2 (769680+24754416 \[Beta]^2-1450449 \[Beta]^4)+6 \[Alpha] \[Beta] (-2384080+44256 \[Beta]^2+703773 \[Beta]^4))+1/107520 (\[Alpha]-\[Beta])^2 (1227 \[Alpha]^7+12873 \[Alpha]^6 \[Beta]-9 \[Alpha]^5 (1732+245 \[Beta]^2)-\[Alpha]^4 \[Beta] (9108+83575 \[Beta]^2)+\[Alpha]^3 (13200+205176 \[Beta]^2-83575 \[Beta]^4)-3 \[Alpha]^2 \[Beta] (58416-68392 \[Beta]^2+735 \[Beta]^4)+\[Beta] (59968+13200 \[Beta]^2-15588 \[Beta]^4+1227 \[Beta]^6)+\[Alpha] (59968-175248 \[Beta]^2-9108 \[Beta]^4+12873 \[Beta]^6))+1/35840 s^2 (132327 \[Alpha]^7-1202187 \[Alpha]^6 \[Beta]+\[Alpha]^5 (816564-2628297 \[Beta]^2)+\[Alpha]^4 \[Beta] (5689956+4477421 \[Beta]^2)+\[Alpha]^3 (-3034416-8690200 \[Beta]^2+4477421 \[Beta]^4)+\[Alpha]^2 (5346224 \[Beta]-8690200 \[Beta]^3-2628297 \[Beta]^5)+\[Alpha] (-1169472+5346224 \[Beta]^2+5689956 \[Beta]^4-1202187 \[Beta]^6)+3 \[Beta] (-389824-1011472 \[Beta]^2+272188 \[Beta]^4+44109 \[Beta]^6))+1/1720320 s (-5533952-882873 \[Alpha]^8+81384 \[Alpha]^7 \[Beta]-11155200 \[Beta]^2+11782176 \[Beta]^4+2846928 \[Beta]^6-882873 \[Beta]^8+24 \[Alpha]^5 \[Beta] (-1275348+30361 \[Beta]^2)+84 \[Alpha]^6 (33892+201789 \[Beta]^2)+8 \[Alpha]^3 \[Beta] (2891568+11401912 \[Beta]^2+91083 \[Beta]^4)-2 \[Alpha]^4 (-5891088+6997992 \[Beta]^2+18024331 \[Beta]^4)+8 \[Alpha] \[Beta] (3748288+2891568 \[Beta]^2-3826044 \[Beta]^4+10173 \[Beta]^6)+12 \[Alpha]^2 (-929600-6683376 \[Beta]^2-1166332 \[Beta]^4+1412523 \[Beta]^6))/.a4->(373248 s^8)/35-62208/5 s^7 (\[Alpha]+\[Beta])+1296/5 s^6 (-32+15 \[Alpha]^2+62 \[Alpha] \[Beta]+15 \[Beta]^2)+54/5 s^5 (500 \[Alpha]+51 \[Alpha]^3+500 \[Beta]-611 \[Alpha]^2 \[Beta]-611 \[Alpha] \[Beta]^2+51 \[Beta]^3)-9/40 s^4 (-7072+2235 \[Alpha]^4-2100 \[Alpha]^3 \[Beta]+1344 \[Beta]^2+2235 \[Beta]^4-28 \[Alpha] \[Beta] (-752+75 \[Beta]^2)-2 \[Alpha]^2 (-672+7871 \[Beta]^2))+3/160 s^3 (3987 \[Alpha]^5+15915 \[Alpha]^4 \[Beta]-10 \[Alpha]^3 (2010+3491 \[Beta]^2)+\[Alpha]^2 (53236 \[Beta]-34910 \[Beta]^3)+\[Beta] (-23168-20100 \[Beta]^2+3987 \[Beta]^4)+\[Alpha] (-23168+53236 \[Beta]^2+15915 \[Beta]^4))+1/17920 3 s^2 (-449024+8547 \[Alpha]^6-381878 \[Alpha]^5 \[Beta]-346832 \[Beta]^2+392504 \[Beta]^4+8547 \[Beta]^6-7 \[Alpha]^4 (-56072+7301 \[Beta]^2)+4 \[Alpha]^3 \[Beta] (91888+281915 \[Beta]^2)-\[Alpha]^2 (346832+2320624 \[Beta]^2+51107 \[Beta]^4)+\[Alpha] (1577056 \[Beta]+367552 \[Beta]^3-381878 \[Beta]^5))+1/327680 3 (44800+3271 \[Alpha]^8+10344 \[Alpha]^7 \[Beta]+98560 \[Beta]^2-31200 \[Beta]^4-26288 \[Beta]^6+3271 \[Beta]^8-8 \[Alpha]^5 \[Beta] (-14692+2693 \[Beta]^2)-4 \[Alpha]^6 (6572+16703 \[Beta]^2)-8 \[Alpha]^3 \[Beta] (23760+54024 \[Beta]^2+2693 \[Beta]^4)+2 \[Alpha]^4 (-15600+62424 \[Beta]^2+74741 \[Beta]^4)+\[Alpha]^2 (98560+442560 \[Beta]^2+124848 \[Beta]^4-66812 \[Beta]^6)+8 \[Alpha] \[Beta] (-24640-23760 \[Beta]^2+14692 \[Beta]^4+1293 \[Beta]^6))-1/143360 3 s (40865 \[Alpha]^7-130781 \[Alpha]^6 \[Beta]-7 \[Alpha]^5 (-2612+81177 \[Beta]^2)+\[Alpha]^4 \[Beta] (1326652+693995 \[Beta]^2)+\[Alpha]^3 (-768592-1470376 \[Beta]^2+693995 \[Beta]^4)+\[Alpha]^2 (952272 \[Beta]-1470376 \[Beta]^3-568239 \[Beta]^5)+\[Alpha] (-172480+952272 \[Beta]^2+1326652 \[Beta]^4-130781 \[Beta]^6)+\[Beta] (-172480-768592 \[Beta]^2+18284 \[Beta]^4+40865 \[Beta]^6))/.a5->-(1/4480)3 (10616832 s^7-9289728 s^6 (\[Alpha]+\[Beta])+516096 s^5 (-13+3 \[Alpha]^2+19 \[Alpha] \[Beta]+3 \[Beta]^2)+322560 s^4 (9 \[Alpha]+2 \[Alpha]^3+9 \[Beta]-9 \[Alpha]^2 \[Beta]-9 \[Alpha] \[Beta]^2+2 \[Beta]^3)-448 s^3 (-2096+495 \[Alpha]^4+60 \[Alpha]^3 \[Beta]-348 \[Beta]^2+495 \[Beta]^4-2 \[Alpha]^2 (174+1483 \[Beta]^2)+\[Alpha] (4648 \[Beta]+60 \[Beta]^3))-(\[Alpha]-\[Beta])^2 (99 \[Alpha]^5+135 \[Alpha]^4 \[Beta]-6 \[Alpha]^3 (56+199 \[Beta]^2)+\[Alpha]^2 (2704 \[Beta]-1194 \[Beta]^3)+3 \[Beta] (-656-112 \[Beta]^2+33 \[Beta]^4)+\[Alpha] (-1968+2704 \[Beta]^2+135 \[Beta]^4))+56 s^2 (219 \[Alpha]^5+2095 \[Alpha]^4 \[Beta]-2 \[Alpha]^3 (1454+1493 \[Beta]^2)+\[Alpha]^2 (4892 \[Beta]-2986 \[Beta]^3)+\[Beta] (-2272-2908 \[Beta]^2+219 \[Beta]^4)+\[Alpha] (-2272+4892 \[Beta]^2+2095 \[Beta]^4))+s (-24512+1519 \[Alpha]^6-11746 \[Alpha]^5 \[Beta]-25904 \[Beta]^2+11004 \[Beta]^4+1519 \[Beta]^6+\[Alpha]^4 (11004-7007 \[Beta]^2)+4 \[Alpha]^3 \[Beta] (6868+9257 \[Beta]^2)-\[Alpha]^2 (25904+86424 \[Beta]^2+7007 \[Beta]^4)+\[Alpha] (67552 \[Beta]+27472 \[Beta]^3-11746 \[Beta]^5)))/.a6->(20736 s^6)/5-2592 s^5 (\[Alpha]+\[Beta])+36 s^4 (-56+3 \[Alpha]^2+62 \[Alpha] \[Beta]+3 \[Beta]^2)+18 s^3 (29 \[Alpha]+10 \[Alpha]^3+29 \[Beta]-25 \[Alpha]^2 \[Beta]-25 \[Alpha] \[Beta]^2+10 \[Beta]^3)-1/40 s^2 (-7352+1125 \[Alpha]^4+1290 \[Alpha]^3 \[Beta]-2946 \[Beta]^2+1125 \[Beta]^4+86 \[Alpha] \[Beta] (146+15 \[Beta]^2)-2 \[Alpha]^2 (1473+3511 \[Beta]^2))+1/256 (-448+29 \[Alpha]^6-110 \[Alpha]^5 \[Beta]-528 \[Beta]^2+60 \[Beta]^4+29 \[Beta]^6+\[Alpha]^4 (60-141 \[Beta]^2)+12 \[Alpha]^3 \[Beta] (44+37 \[Beta]^2)-22 \[Alpha] \[Beta] (-48-24 \[Beta]^2+5 \[Beta]^4)-3 \[Alpha]^2 (176+392 \[Beta]^2+47 \[Beta]^4))-1/320 s (57 \[Alpha]^5-3995 \[Alpha]^4 \[Beta]+\[Alpha]^3 (5864+4258 \[Beta]^2)+\[Alpha]^2 (-7144 \[Beta]+4258 \[Beta]^3)+\[Alpha] (2640-7144 \[Beta]^2-3995 \[Beta]^4)+\[Beta] (2640+5864 \[Beta]^2+57 \[Beta]^4))/.a7->-(3/80) (55296 s^5-23040 s^4 (\[Alpha]+\[Beta])-480 s^3 (40+3 \[Alpha]^2-34 \[Alpha] \[Beta]+3 \[Beta]^2)+20 s^2 (124 \[Alpha]+63 \[Alpha]^3+124 \[Beta]-103 \[Alpha]^2 \[Beta]-103 \[Alpha] \[Beta]^2+63 \[Beta]^3)-(\[Alpha]-\[Beta])^2 (3 \[Alpha]^3-19 \[Alpha]^2 \[Beta]+\[Alpha] (36-19 \[Beta]^2)+3 \[Beta] (12+\[Beta]^2))+s (944-75 \[Alpha]^4-220 \[Alpha]^3 \[Beta]+512 \[Beta]^2-75 \[Beta]^4-4 \[Alpha] \[Beta] (328+55 \[Beta]^2)+\[Alpha]^2 (512+654 \[Beta]^2)))/.a8->3/128 (144+36864 s^4-3 \[Alpha]^4-36 \[Alpha]^3 \[Beta]+88 \[Beta]^2-3 \[Beta]^4-9216 s^3 (\[Alpha]+\[Beta])-4 \[Alpha] \[Beta] (44+9 \[Beta]^2)-64 s^2 (128+21 \[Alpha]^2-86 \[Alpha] \[Beta]+21 \[Beta]^2)+\[Alpha]^2 (88+78 \[Beta]^2)+8 s (44 \[Alpha]+39 \[Alpha]^3+44 \[Beta]-47 \[Alpha]^2 \[Beta]-47 \[Alpha] \[Beta]^2+39 \[Beta]^3))/.a9->1/2 (-576 s^3+72 s^2 (\[Alpha]+\[Beta])-(\[Alpha]-\[Beta])^2 (\[Alpha]+\[Beta])+s (68+15 \[Alpha]^2-38 \[Alpha] \[Beta]+15 \[Beta]^2))/.a10->3/4 (-4+96 s^2-\[Alpha]^2+2 \[Alpha] \[Beta]-\[Beta]^2-4 s (\[Alpha]+\[Beta]))//Simplify;
Coefficient[R12alphabeta[x],x,12]//Simplify
1
Coefficient[R12alphabeta[x],x,11]//Simplify
-12 s
Coefficient[R12alphabeta[x],x,10]//Simplify
72 s^2-3 s (\[Alpha]+\[Beta])-3/4 (4+\[Alpha]^2-2 \[Alpha] \[Beta]+\[Beta]^2)
Coefficient[R12alphabeta[x],x,9]//Simplify
1/2 (-576 s^3+72 s^2 (\[Alpha]+\[Beta])-(\[Alpha]-\[Beta])^2 (\[Alpha]+\[Beta])+s (68+15 \[Alpha]^2-38 \[Alpha] \[Beta]+15 \[Beta]^2))
Coefficient[%1,x,8]//Simplify
3/128 (144+36864 s^4-3 \[Alpha]^4-36 \[Alpha]^3 \[Beta]+88 \[Beta]^2-3 \[Beta]^4-9216 s^3 (\[Alpha]+\[Beta])-4 \[Alpha] \[Beta] (44+9 \[Beta]^2)-64 s^2 (128+21 \[Alpha]^2-86 \[Alpha] \[Beta]+21 \[Beta]^2)+\[Alpha]^2 (88+78 \[Beta]^2)+8 s (44 \[Alpha]+39 \[Alpha]^3+44 \[Beta]-47 \[Alpha]^2 \[Beta]-47 \[Alpha] \[Beta]^2+39 \[Beta]^3))
Coefficient[R12alphabeta[x],x,7]//Simplify
3/80 (-55296 s^5+23040 s^4 (\[Alpha]+\[Beta])+480 s^3 (40+3 \[Alpha]^2-34 \[Alpha] \[Beta]+3 \[Beta]^2)-20 s^2 (124 \[Alpha]+63 \[Alpha]^3+124 \[Beta]-103 \[Alpha]^2 \[Beta]-103 \[Alpha] \[Beta]^2+63 \[Beta]^3)+(\[Alpha]-\[Beta])^2 (3 \[Alpha]^3-19 \[Alpha]^2 \[Beta]+\[Alpha] (36-19 \[Beta]^2)+3 \[Beta] (12+\[Beta]^2))+s (-944+75 \[Alpha]^4+220 \[Alpha]^3 \[Beta]-512 \[Beta]^2+75 \[Beta]^4+4 \[Alpha] \[Beta] (328+55 \[Beta]^2)-2 \[Alpha]^2 (256+327 \[Beta]^2)))
Coefficient[R12alphabeta[x],x,6]//Simplify
(20736 s^6)/5-2592 s^5 (\[Alpha]+\[Beta])+36 s^4 (-56+3 \[Alpha]^2+62 \[Alpha] \[Beta]+3 \[Beta]^2)+18 s^3 (29 \[Alpha]+10 \[Alpha]^3+29 \[Beta]-25 \[Alpha]^2 \[Beta]-25 \[Alpha] \[Beta]^2+10 \[Beta]^3)-1/40 s^2 (-7352+1125 \[Alpha]^4+1290 \[Alpha]^3 \[Beta]-2946 \[Beta]^2+1125 \[Beta]^4+86 \[Alpha] \[Beta] (146+15 \[Beta]^2)-2 \[Alpha]^2 (1473+3511 \[Beta]^2))+1/256 (-448+29 \[Alpha]^6-110 \[Alpha]^5 \[Beta]-528 \[Beta]^2+60 \[Beta]^4+29 \[Beta]^6+\[Alpha]^4 (60-141 \[Beta]^2)+12 \[Alpha]^3 \[Beta] (44+37 \[Beta]^2)-22 \[Alpha] \[Beta] (-48-24 \[Beta]^2+5 \[Beta]^4)-3 \[Alpha]^2 (176+392 \[Beta]^2+47 \[Beta]^4))-1/320 s (57 \[Alpha]^5-3995 \[Alpha]^4 \[Beta]+\[Alpha]^3 (5864+4258 \[Beta]^2)+\[Alpha]^2 (-7144 \[Beta]+4258 \[Beta]^3)+\[Alpha] (2640-7144 \[Beta]^2-3995 \[Beta]^4)+\[Beta] (2640+5864 \[Beta]^2+57 \[Beta]^4))
Coefficient[R12alphabeta[x],x,5]//Simplify
-1/4480 3 (10616832 s^7-9289728 s^6 (\[Alpha]+\[Beta])+516096 s^5 (-13+3 \[Alpha]^2+19 \[Alpha] \[Beta]+3 \[Beta]^2)+322560 s^4 (9 \[Alpha]+2 \[Alpha]^3+9 \[Beta]-9 \[Alpha]^2 \[Beta]-9 \[Alpha] \[Beta]^2+2 \[Beta]^3)-448 s^3 (-2096+495 \[Alpha]^4+60 \[Alpha]^3 \[Beta]-348 \[Beta]^2+495 \[Beta]^4-2 \[Alpha]^2 (174+1483 \[Beta]^2)+\[Alpha] (4648 \[Beta]+60 \[Beta]^3))-(\[Alpha]-\[Beta])^2 (99 \[Alpha]^5+135 \[Alpha]^4 \[Beta]-6 \[Alpha]^3 (56+199 \[Beta]^2)+\[Alpha]^2 (2704 \[Beta]-1194 \[Beta]^3)+3 \[Beta] (-656-112 \[Beta]^2+33 \[Beta]^4)+\[Alpha] (-1968+2704 \[Beta]^2+135 \[Beta]^4))+56 s^2 (219 \[Alpha]^5+2095 \[Alpha]^4 \[Beta]-2 \[Alpha]^3 (1454+1493 \[Beta]^2)+\[Alpha]^2 (4892 \[Beta]-2986 \[Beta]^3)+\[Beta] (-2272-2908 \[Beta]^2+219 \[Beta]^4)+\[Alpha] (-2272+4892 \[Beta]^2+2095 \[Beta]^4))+s (-24512+1519 \[Alpha]^6-11746 \[Alpha]^5 \[Beta]-25904 \[Beta]^2+11004 \[Beta]^4+1519 \[Beta]^6+\[Alpha]^4 (11004-7007 \[Beta]^2)+4 \[Alpha]^3 \[Beta] (6868+9257 \[Beta]^2)-\[Alpha]^2 (25904+86424 \[Beta]^2+7007 \[Beta]^4)+\[Alpha] (67552 \[Beta]+27472 \[Beta]^3-11746 \[Beta]^5)))
Coefficient[R12alphabeta[x],x,4]//Simplify
(373248 s^8)/35-62208/5 s^7 (\[Alpha]+\[Beta])+1296/5 s^6 (-32+15 \[Alpha]^2+62 \[Alpha] \[Beta]+15 \[Beta]^2)+54/5 s^5 (500 \[Alpha]+51 \[Alpha]^3+500 \[Beta]-611 \[Alpha]^2 \[Beta]-611 \[Alpha] \[Beta]^2+51 \[Beta]^3)-9/40 s^4 (-7072+2235 \[Alpha]^4-2100 \[Alpha]^3 \[Beta]+1344 \[Beta]^2+2235 \[Beta]^4-28 \[Alpha] \[Beta] (-752+75 \[Beta]^2)-2 \[Alpha]^2 (-672+7871 \[Beta]^2))+3/160 s^3 (3987 \[Alpha]^5+15915 \[Alpha]^4 \[Beta]-10 \[Alpha]^3 (2010+3491 \[Beta]^2)+\[Alpha]^2 (53236 \[Beta]-34910 \[Beta]^3)+\[Beta] (-23168-20100 \[Beta]^2+3987 \[Beta]^4)+\[Alpha] (-23168+53236 \[Beta]^2+15915 \[Beta]^4))+1/17920 3 s^2 (-449024+8547 \[Alpha]^6-381878 \[Alpha]^5 \[Beta]-346832 \[Beta]^2+392504 \[Beta]^4+8547 \[Beta]^6-7 \[Alpha]^4 (-56072+7301 \[Beta]^2)+4 \[Alpha]^3 \[Beta] (91888+281915 \[Beta]^2)-\[Alpha]^2 (346832+2320624 \[Beta]^2+51107 \[Beta]^4)+\[Alpha] (1577056 \[Beta]+367552 \[Beta]^3-381878 \[Beta]^5))+1/327680 3 (44800+3271 \[Alpha]^8+10344 \[Alpha]^7 \[Beta]+98560 \[Beta]^2-31200 \[Beta]^4-26288 \[Beta]^6+3271 \[Beta]^8-8 \[Alpha]^5 \[Beta] (-14692+2693 \[Beta]^2)-4 \[Alpha]^6 (6572+16703 \[Beta]^2)-8 \[Alpha]^3 \[Beta] (23760+54024 \[Beta]^2+2693 \[Beta]^4)+2 \[Alpha]^4 (-15600+62424 \[Beta]^2+74741 \[Beta]^4)+\[Alpha]^2 (98560+442560 \[Beta]^2+124848 \[Beta]^4-66812 \[Beta]^6)+8 \[Alpha] \[Beta] (-24640-23760 \[Beta]^2+14692 \[Beta]^4+1293 \[Beta]^6))-1/143360 3 s (40865 \[Alpha]^7-130781 \[Alpha]^6 \[Beta]-7 \[Alpha]^5 (-2612+81177 \[Beta]^2)+\[Alpha]^4 \[Beta] (1326652+693995 \[Beta]^2)+\[Alpha]^3 (-768592-1470376 \[Beta]^2+693995 \[Beta]^4)+\[Alpha]^2 (952272 \[Beta]-1470376 \[Beta]^3-568239 \[Beta]^5)+\[Alpha] (-172480+952272 \[Beta]^2+1326652 \[Beta]^4-130781 \[Beta]^6)+\[Beta] (-172480-768592 \[Beta]^2+18284 \[Beta]^4+40865 \[Beta]^6))
Coefficient[R12alphabeta[x],x,3]//Simplify
-((497664 s^9)/35)+746496/35 s^8 (\[Alpha]+\[Beta])-5184/35 s^7 (-88+69 \[Alpha]^2+226 \[Alpha] \[Beta]+69 \[Beta]^2)+648/5 s^6 (-92 \[Alpha]+3 \[Alpha]^3-92 \[Beta]+141 \[Alpha]^2 \[Beta]+141 \[Alpha] \[Beta]^2+3 \[Beta]^3)+9/10 s^5 (-3520+1287 \[Alpha]^4-3396 \[Alpha]^3 \[Beta]+2496 \[Beta]^2+1287 \[Beta]^4+\[Alpha]^2 (2496-12886 \[Beta]^2)-4 \[Alpha] \[Beta] (-3584+849 \[Beta]^2))-9/40 s^4 (1533 \[Alpha]^5+3045 \[Alpha]^4 \[Beta]-6 \[Alpha]^3 (586+2187 \[Beta]^2)-2 \[Alpha]^2 \[Beta] (-8902+6561 \[Beta]^2)+\[Beta] (-6464-3516 \[Beta]^2+1533 \[Beta]^4)+\[Alpha] (-6464+17804 \[Beta]^2+3045 \[Beta]^4))+1/13440 s^3 (2995712+309393 \[Alpha]^6+4222638 \[Alpha]^5 \[Beta]+769680 \[Beta]^2-4189752 \[Beta]^4+309393 \[Beta]^6-63 \[Alpha]^4 (66504+23023 \[Beta]^2)-4 \[Alpha]^3 \[Beta] (-66384+3430775 \[Beta]^2)+\[Alpha]^2 (769680+24754416 \[Beta]^2-1450449 \[Beta]^4)+6 \[Alpha] \[Beta] (-2384080+44256 \[Beta]^2+703773 \[Beta]^4))+1/107520 (\[Alpha]-\[Beta])^2 (1227 \[Alpha]^7+12873 \[Alpha]^6 \[Beta]-9 \[Alpha]^5 (1732+245 \[Beta]^2)-\[Alpha]^4 \[Beta] (9108+83575 \[Beta]^2)+\[Alpha]^3 (13200+205176 \[Beta]^2-83575 \[Beta]^4)-3 \[Alpha]^2 \[Beta] (58416-68392 \[Beta]^2+735 \[Beta]^4)+\[Beta] (59968+13200 \[Beta]^2-15588 \[Beta]^4+1227 \[Beta]^6)+\[Alpha] (59968-175248 \[Beta]^2-9108 \[Beta]^4+12873 \[Beta]^6))+1/35840 s^2 (132327 \[Alpha]^7-1202187 \[Alpha]^6 \[Beta]+\[Alpha]^5 (816564-2628297 \[Beta]^2)+\[Alpha]^4 \[Beta] (5689956+4477421 \[Beta]^2)+\[Alpha]^3 (-3034416-8690200 \[Beta]^2+4477421 \[Beta]^4)+\[Alpha]^2 (5346224 \[Beta]-8690200 \[Beta]^3-2628297 \[Beta]^5)+\[Alpha] (-1169472+5346224 \[Beta]^2+5689956 \[Beta]^4-1202187 \[Beta]^6)+3 \[Beta] (-389824-1011472 \[Beta]^2+272188 \[Beta]^4+44109 \[Beta]^6))-1/1720320 s (5533952+882873 \[Alpha]^8-81384 \[Alpha]^7 \[Beta]+11155200 \[Beta]^2-11782176 \[Beta]^4-2846928 \[Beta]^6+882873 \[Beta]^8-84 \[Alpha]^6 (33892+201789 \[Beta]^2)+\[Alpha]^5 (30608352 \[Beta]-728664 \[Beta]^3)-8 \[Alpha]^3 \[Beta] (2891568+11401912 \[Beta]^2+91083 \[Beta]^4)+2 \[Alpha]^4 (-5891088+6997992 \[Beta]^2+18024331 \[Beta]^4)-8 \[Alpha] \[Beta] (3748288+2891568 \[Beta]^2-3826044 \[Beta]^4+10173 \[Beta]^6)-12 \[Alpha]^2 (-929600-6683376 \[Beta]^2-1166332 \[Beta]^4+1412523 \[Beta]^6))
Coefficient[R12alphabeta[x],x,2]//Simplify
1/45875200 (782757789696 s^10-1467670855680 s^9 (\[Alpha]+\[Beta])+163074539520 s^8 (-5+6 \[Alpha]^2+17 \[Alpha] \[Beta]+6 \[Beta]^2)-10192158720 s^7 (-98 \[Alpha]+19 \[Alpha]^3-98 \[Beta]+191 \[Alpha]^2 \[Beta]+191 \[Alpha] \[Beta]^2+19 \[Beta]^3)+49545216 s^6 (4768-1575 \[Alpha]^4+10860 \[Alpha]^3 \[Beta]-6936 \[Beta]^2-1575 \[Beta]^4+4 \[Alpha] \[Beta] (-6716+2715 \[Beta]^2)+\[Alpha]^2 (-6936+29638 \[Beta]^2))+6193152 s^5 (7707 \[Alpha]^5+3775 \[Alpha]^4 \[Beta]-2 \[Alpha]^3 (2708+39941 \[Beta]^2)+\[Alpha]^2 (92936 \[Beta]-79882 \[Beta]^3)+\[Alpha] (-26560+92936 \[Beta]^2+3775 \[Beta]^4)+\[Beta] (-26560-5416 \[Beta]^2+7707 \[Beta]^4))+20480 s^4 (-1070080-397467 \[Alpha]^6-2316762 \[Alpha]^5 \[Beta]+646416 \[Beta]^2+2097144 \[Beta]^4-397467 \[Beta]^6+63 \[Alpha]^4 (33288+38821 \[Beta]^2)+4 \[Alpha]^3 \[Beta] (-639648+2450029 \[Beta]^2)-6 \[Alpha] \[Beta] (-1211312+426432 \[Beta]^2+386127 \[Beta]^4)+3 \[Alpha]^2 (215472-5095504 \[Beta]^2+815241 \[Beta]^4))+30720 s^3 (27 \[Alpha]^7+318864 \[Alpha]^6 \[Beta]-65 \[Alpha]^4 \[Beta] (12197+17369 \[Beta]^2)+7 \[Alpha]^5 (-35607+56162 \[Beta]^2)+\[Alpha]^3 (374120+1976646 \[Beta]^2-1128985 \[Beta]^4)+2 \[Alpha]^2 \[Beta] (-547452+988323 \[Beta]^2+196567 \[Beta]^4)+\[Beta] (213232+374120 \[Beta]^2-249249 \[Beta]^4+27 \[Beta]^6)+\[Alpha] (213232-1094904 \[Beta]^2-792805 \[Beta]^4+318864 \[Beta]^6))+32 s^2 (17055488+4412745 \[Alpha]^8-17086320 \[Alpha]^7 \[Beta]+24613248 \[Beta]^2-74425728 \[Beta]^4+2961000 \[Beta]^6+4412745 \[Beta]^8+5040 \[Alpha]^5 \[Beta] (37101+5441 \[Beta]^2)-420 \[Alpha]^6 (-7050+257357 \[Beta]^2)+16 \[Alpha]^3 \[Beta] (-2985624-33881438 \[Beta]^2+1713915 \[Beta]^4)+\[Alpha]^4 (-74425728+979608 \[Beta]^2+245082518 \[Beta]^4)-16 \[Alpha] \[Beta] (7923728+2985624 \[Beta]^2-11686815 \[Beta]^4+1067895 \[Beta]^6)-12 \[Alpha]^2 (-2051104-33995136 \[Beta]^2-81634 \[Beta]^4+9007495 \[Beta]^6))+3 (-537600+58923 \[Alpha]^10+980850 \[Alpha]^9 \[Beta]-2464000 \[Beta]^2+2352000 \[Beta]^4+2368992 \[Beta]^6-1072708 \[Beta]^8+58923 \[Beta]^10-696 \[Alpha]^7 \[Beta] (2452+11571 \[Beta]^2)-13 \[Alpha]^8 (82516+51957 \[Beta]^2)+\[Alpha]^6 (2368992+20133776 \[Beta]^2+482118 \[Beta]^4)+4 \[Alpha]^5 \[Beta] (-3586896+1042648 \[Beta]^2+3603483 \[Beta]^4)+8 \[Alpha]^3 \[Beta] (1108800+5804496 \[Beta]^2+521324 \[Beta]^4-1006677 \[Beta]^6)+2 \[Alpha]^4 (1176000-5619696 \[Beta]^2-21525068 \[Beta]^4+241059 \[Beta]^6)+2 \[Alpha] \[Beta] (2464000+4435200 \[Beta]^2-7173792 \[Beta]^4-853296 \[Beta]^6+490425 \[Beta]^8)-\[Alpha]^2 (2464000+22444800 \[Beta]^2+11239392 \[Beta]^4-20133776 \[Beta]^6+675441 \[Beta]^8))-4 s (3041475 \[Alpha]^9+8524395 \[Alpha]^8 \[Beta]-12 \[Alpha]^7 (1438196+5200907 \[Beta]^2)+\[Alpha]^6 (82326192 \[Beta]-90084500 \[Beta]^3)+2 \[Alpha]^4 \[Beta] (-116768496-174627816 \[Beta]^2+73905397 \[Beta]^4)+2 \[Alpha]^5 (-7314864+130911816 \[Beta]^2+73905397 \[Beta]^4)-4 \[Alpha]^2 \[Beta] (21101888-69138000 \[Beta]^2-65455908 \[Beta]^4+15602721 \[Beta]^6)-4 \[Alpha]^3 (-16532288-69138000 \[Beta]^2+87313908 \[Beta]^4+22521125 \[Beta]^6)+\[Beta] (7392000+66129152 \[Beta]^2-14629728 \[Beta]^4-17258352 \[Beta]^6+3041475 \[Beta]^8)+\[Alpha] (7392000-84407552 \[Beta]^2-233536992 \[Beta]^4+82326192 \[Beta]^6+8524395 \[Beta]^8)))
Coefficient[R12alphabeta[x],x,1]//Simplify
1/137625600 (-2336247 \[Alpha]^11-2348273369088 s^10 (1+\[Alpha])-3 \[Alpha]^10 (778749+120310 \[Beta])-3 \[Alpha]^9 (-954384+120310 \[Beta]+1554237 \[Beta]^2)+\[Alpha]^8 (4433712+5998848 \[Beta]-4662711 \[Beta]^2-105301816 \[Beta]^3)-2 \[Alpha]^7 (-366576-9667584 \[Beta]-99541248 \[Beta]^2+52650908 \[Beta]^3+102409111 \[Beta]^4)-2 \[Alpha]^6 (5047824+52664352 \[Beta]-82437888 \[Beta]^2-207023296 \[Beta]^3+102409111 \[Beta]^4+18641014 \[Beta]^5)+2 \[Alpha]^5 (6212480-41443872 \[Beta]-166652976 \[Beta]^2+164596416 \[Beta]^3-19720528 \[Beta]^4-18641014 \[Beta]^5+77456749 \[Beta]^6)+2 \[Alpha]^4 (6919040+61120000 \[Beta]-96557616 \[Beta]^2+50658624 \[Beta]^3+32356272 \[Beta]^4-164105344 \[Beta]^5+77456749 \[Beta]^6+42265092 \[Beta]^7)-\[Beta]^2 (-1209600+12369920 \[Beta]+4435200 \[Beta]^2+1413120 \[Beta]^3+3788448 \[Beta]^4-10828800 \[Beta]^5-5532912 \[Beta]^6+1570560 \[Beta]^7+530307 \[Beta]^8)-\[Alpha]^3 (15998720-46238720 \[Beta]+58186240 \[Beta]^2+50485632 \[Beta]^3-264184608 \[Beta]^4+224057088 \[Beta]^5+17075584 \[Beta]^6-84530184 \[Beta]^7+11378811 \[Beta]^8)-\[Alpha] \[Beta] (2419200-13579520 \[Beta]+20433920 \[Beta]^2-71566080 \[Beta]^3-38755776 \[Beta]^4+26229408 \[Beta]^5-13154688 \[Beta]^6+7803408 \[Beta]^7+10398210 \[Beta]^8+530307 \[Beta]^9)-\[Alpha]^2 (3628800-9950720 \[Beta]-16401920 \[Beta]^2+95022080 \[Beta]^3-112381728 \[Beta]^4+101434944 \[Beta]^5+101929344 \[Beta]^6-47361408 \[Beta]^7+11378811 \[Beta]^8+10398210 \[Beta]^9)+489223618560 s^9 (4+13 \[Alpha]^2+9 \[Beta]+\[Alpha] (13+9 \[Beta]))-489223618560 s^8 (-2+15 \[Alpha]^3+6 \[Beta]+6 \[Beta]^2+\[Alpha]^2 (15+23 \[Beta])+\[Alpha] (4+23 \[Beta]+6 \[Beta]^2))+10192158720 s^7 (-80+459 \[Alpha]^4-126 \[Beta]+138 \[Beta]^2+57 \[Beta]^3+\[Alpha]^3 (459+1193 \[Beta])+\[Alpha]^2 (-68+1193 \[Beta]+711 \[Beta]^2)+\[Alpha] (-206+326 \[Beta]+711 \[Beta]^2+57 \[Beta]^3))-148635648 s^6 (928+11985 \[Alpha]^5-5280 \[Beta]-3336 \[Beta]^2+360 \[Beta]^3-1575 \[Beta]^4+15 \[Alpha]^4 (799+3228 \[Beta])+2 \[Alpha]^3 (-6048+24210 \[Beta]+25079 \[Beta]^2)+2 \[Alpha]^2 (-6228-172 \[Beta]+25079 \[Beta]^2+5610 \[Beta]^3)+\[Alpha] (-4352-17264 \[Beta]+13584 \[Beta]^2+11220 \[Beta]^3-1575 \[Beta]^4))+6193152 s^5 (16640+65619 \[Alpha]^6+17280 \[Beta]-26880 \[Beta]^2+4008 \[Beta]^3-25740 \[Beta]^4-23121 \[Beta]^5+207 \[Alpha]^5 (317+1965 \[Beta])+23 \[Alpha]^4 (-7164+17685 \[Beta]+29002 \[Beta]^2)+2 \[Alpha]^3 (-69516-133724 \[Beta]+333523 \[Beta]^2+147663 \[Beta]^3)+\[Alpha]^2 (7040-335368 \[Beta]+98672 \[Beta]^2+295326 \[Beta]^3-37065 \[Beta]^4)-\[Alpha] (-33920+123520 \[Beta]+159048 \[Beta]^2-71928 \[Beta]^3+37065 \[Beta]^4+23121 \[Beta]^5))-61440 s^4 (-86272+848421 \[Alpha]^7+838656 \[Beta]+210960 \[Beta]^2+804384 \[Beta]^3+970704 \[Beta]^4-772632 \[Beta]^5-397467 \[Beta]^6+63 \[Alpha]^6 (13467+134866 \[Beta])+63 \[Alpha]^5 (-70360+134866 \[Beta]+342693 \[Beta]^2)+\[Alpha]^4 (-3660048-15685272 \[Beta]+21589659 \[Beta]^2+16504324 \[Beta]^3)+\[Alpha]^3 (2837808-14150592 \[Beta]-5793168 \[Beta]^2+16504324 \[Beta]^3-215397 \[Beta]^4)-3 \[Alpha]^2 (-677808+708224 \[Beta]+4135552 \[Beta]^2-1972560 \[Beta]^3+71799 \[Beta]^4+1029798 \[Beta]^5)-\[Alpha] (-752384-2493984 \[Beta]+4407696 \[Beta]^2+695808 \[Beta]^3+563976 \[Beta]^4+3089394 \[Beta]^5+397467 \[Beta]^6))+10240 s^3 (-350720+318600 \[Alpha]^8-193392 \[Beta]-92304 \[Beta]^2-721080 \[Beta]^3+2193912 \[Beta]^4+1238517 \[Beta]^5-309393 \[Beta]^6-243 \[Beta]^7+54 \[Alpha]^7 (5900+107989 \[Beta])+189 \[Alpha]^6 (-18372+30854 \[Beta]+126935 \[Beta]^2)+7 \[Alpha]^5 (-451845-3371571 \[Beta]+3427245 \[Beta]^2+4288595 \[Beta]^3)+\[Alpha]^4 (5751216-19378359 \[Beta]-27027645 \[Beta]^2+30020165 \[Beta]^3+5604894 \[Beta]^4)+\[Alpha]^3 (3557304+7493928 \[Beta]-28478094 \[Beta]^2+6869150 \[Beta]^3+5604894 \[Beta]^4-8765568 \[Beta]^5)-\[Alpha]^2 (636416-8001384 \[Beta]+10401144 \[Beta]^2+6853950 \[Beta]^3-6769026 \[Beta]^4+8765568 \[Beta]^5+3179169 \[Beta]^6)-\[Alpha] (544112-3595632 \[Beta]-2394360 \[Beta]^2+1228536 \[Beta]^3-5318577 \[Beta]^4+2984121 \[Beta]^5+3179169 \[Beta]^6+243 \[Beta]^7))-96 s^2 (1596465 \[Alpha]^9+15 \[Alpha]^8 (106431+2106952 \[Beta])+20 \[Alpha]^7 (-982452+1580214 \[Beta]+12614777 \[Beta]^2)+20 \[Alpha]^6 (-1247106-14741770 \[Beta]+12614777 \[Beta]^2+26185702 \[Beta]^3)+\[Alpha]^5 (76641952-246747920 \[Beta]-700601952 \[Beta]^2+523714040 \[Beta]^3+258966478 \[Beta]^4)-2 \[Alpha]^4 (-27876416-162314448 \[Beta]+297735036 \[Beta]^2+74436524 \[Beta]^3-129483239 \[Beta]^4+90566700 \[Beta]^5)-4 \[Alpha]^3 (13408448-52414464 \[Beta]+11408272 \[Beta]^2+81992472 \[Beta]^3-84165692 \[Beta]^4+45283350 \[Beta]^5+38531535 \[Beta]^6)-4 \[Alpha]^2 (5213408-10472608 \[Beta]-35361888 \[Beta]^2+56412976 \[Beta]^3-39391482 \[Beta]^4-2773890 \[Beta]^5+38531535 \[Beta]^6+2948310 \[Beta]^7)+3 (251136-2117120 \[Beta]+599936 \[Beta]^2-10926720 \[Beta]^3-6848256 \[Beta]^4+6963040 \[Beta]^5+1670760 \[Beta]^6+1764360 \[Beta]^7+1470915 \[Beta]^8)+\[Alpha] (-5597952-19710208 \[Beta]+63400448 \[Beta]^2-38571264 \[Beta]^3+94426272 \[Beta]^4+116227440 \[Beta]^5-43075200 \[Beta]^6-11793240 \[Beta]^7+4412745 \[Beta]^8))+4 s (6968320+7014285 \[Alpha]^10+1209600 \[Beta]+28830720 \[Beta]^2+23901696 \[Beta]^3-78879360 \[Beta]^4-24596064 \[Beta]^5-21940800 \[Beta]^6-22352256 \[Beta]^7+17657460 \[Beta]^8+9124425 \[Beta]^9+15 \[Alpha]^9 (467619+393823 \[Beta])+3 \[Alpha]^8 (-2232452+1969115 \[Beta]+83327996 \[Beta]^2)+12 \[Alpha]^7 (-2029568-26428872 \[Beta]+20831999 \[Beta]^2+82528775 \[Beta]^3)+2 \[Alpha]^6 (35044848-157759392 \[Beta]-827396232 \[Beta]^2+495172650 \[Beta]^3+488165171 \[Beta]^4)-2 \[Alpha]^5 (-46015248-447144912 \[Beta]+657893472 \[Beta]^2+703346288 \[Beta]^3-488165171 \[Beta]^4+122386089 \[Beta]^5)-2 \[Alpha]^4 (75412032-276375312 \[Beta]-415174080 \[Beta]^2+696059648 \[Beta]^3-486886172 \[Beta]^4+122386089 \[Beta]^5+334211790 \[Beta]^6)-4 \[Alpha]^3 (17986176+62354944 \[Beta]-177967440 \[Beta]^2+257602480 \[Beta]^3-63199776 \[Beta]^4-180649464 \[Beta]^5+167105895 \[Beta]^6+39859383 \[Beta]^7)+\[Alpha]^2 (37008640-135870976 \[Beta]+452945664 \[Beta]^2-59229120 \[Beta]^3-135364896 \[Beta]^4+737171136 \[Beta]^5-208130064 \[Beta]^6-159437532 \[Beta]^7+43230645 \[Beta]^8)+\[Alpha] (8177920-81191680 \[Beta]-3672576 \[Beta]^2-89647104 \[Beta]^3-253843296 \[Beta]^4+316943136 \[Beta]^5+130875456 \[Beta]^6-23979936 \[Beta]^7+43230645 \[Beta]^8+9124425 \[Beta]^9)))
Coefficient[R12alphabeta[x],x,0]//Simplify
1/45875200 (-782757789696 s^10+1467670855680 s^9 (\[Alpha]+\[Beta])-163074539520 s^8 (-2+6 \[Alpha]^2+17 \[Alpha] \[Beta]+6 \[Beta]^2)+10192158720 s^7 (-42 \[Alpha]+19 \[Alpha]^3-42 \[Beta]+191 \[Alpha]^2 \[Beta]+191 \[Alpha] \[Beta]^2+19 \[Beta]^3)+49545216 s^6 (-928+1575 \[Alpha]^4-10860 \[Alpha]^3 \[Beta]+3336 \[Beta]^2+1575 \[Beta]^4+\[Alpha]^2 (3336-29638 \[Beta]^2)-4 \[Alpha] \[Beta] (-2996+2715 \[Beta]^2))-6193152 s^5 (7707 \[Alpha]^5+3775 \[Alpha]^4 \[Beta]-2 \[Alpha]^3 (668+39941 \[Beta]^2)+\[Alpha]^2 (44056 \[Beta]-79882 \[Beta]^3)+\[Alpha] (-5760+44056 \[Beta]^2+3775 \[Beta]^4)+\[Beta] (-5760-1336 \[Beta]^2+7707 \[Beta]^4))+20480 s^4 (86272+397467 \[Alpha]^6+2316762 \[Alpha]^5 \[Beta]-210960 \[Beta]^2-970704 \[Beta]^4+397467 \[Beta]^6-63 \[Alpha]^4 (15408+38821 \[Beta]^2)+\[Alpha]^3 (1500192 \[Beta]-9800116 \[Beta]^3)+6 \[Alpha] \[Beta] (-275888+250032 \[Beta]^2+386127 \[Beta]^4)-3 \[Alpha]^2 (70320-2450848 \[Beta]^2+815241 \[Beta]^4))-30720 s^3 (27 \[Alpha]^7+318864 \[Alpha]^6 \[Beta]+7 \[Alpha]^5 (-19659+56162 \[Beta]^2)-5 \[Alpha]^4 \[Beta] (69437+225797 \[Beta]^2)+\[Alpha]^3 (80120+999166 \[Beta]^2-1128985 \[Beta]^4)+\[Alpha]^2 (-276296 \[Beta]+999166 \[Beta]^3+393134 \[Beta]^5)+\[Beta] (21488+80120 \[Beta]^2-137613 \[Beta]^4+27 \[Beta]^6)+\[Alpha] (21488-276296 \[Beta]^2-347185 \[Beta]^4+318864 \[Beta]^6))-(\[Alpha]-\[Beta])^2 (-403200+176769 \[Alpha]^8+3296088 \[Alpha]^7 \[Beta]+1478400 \[Beta]^2+1262816 \[Beta]^4-1844304 \[Beta]^6+176769 \[Beta]^8+84 \[Alpha]^6 (-21956+52251 \[Beta]^2)-24 \[Alpha]^5 \[Beta] (185996+778257 \[Beta]^2)+\[Alpha]^4 (1262816+25256784 \[Beta]^2-40299066 \[Beta]^4)-8 \[Alpha]^3 \[Beta] (1358000-7305096 \[Beta]^2+2334771 \[Beta]^4)+8 \[Alpha] \[Beta] (705600-1358000 \[Beta]^2-557988 \[Beta]^4+412011 \[Beta]^6)+4 \[Alpha]^2 (369600-7385008 \[Beta]^2+6314196 \[Beta]^4+1097271 \[Beta]^6))+32 s^2 (-4412745 \[Alpha]^8+17086320 \[Alpha]^7 \[Beta]-1680 \[Alpha]^5 \[Beta] (56749+16323 \[Beta]^2)+420 \[Alpha]^6 (-11934+257357 \[Beta]^2)+\[Alpha]^4 (20544768+11286072 \[Beta]^2-245082518 \[Beta]^4)+16 \[Alpha]^3 \[Beta] (361944+16966538 \[Beta]^2-1713915 \[Beta]^4)+16 \[Alpha] \[Beta] (834928+361944 \[Beta]^2-5958645 \[Beta]^4+1067895 \[Beta]^6)+4 \[Alpha]^2 (-449952-25665088 \[Beta]^2+2821518 \[Beta]^4+27022485 \[Beta]^6)-3 (251136+599936 \[Beta]^2-6848256 \[Beta]^4+1670760 \[Beta]^6+1470915 \[Beta]^8))+4 s (3041475 \[Alpha]^9+403200 \[Beta]+8524395 \[Alpha]^8 \[Beta]+7967232 \[Beta]^3-8198688 \[Beta]^5-7450752 \[Beta]^7+3041475 \[Beta]^9-12 \[Alpha]^7 (620896+5200907 \[Beta]^2)+\[Alpha]^6 (50938752 \[Beta]-90084500 \[Beta]^3)+2 \[Alpha]^4 \[Beta] (-29160656-91348416 \[Beta]^2+73905397 \[Beta]^4)+2 \[Alpha]^5 (-4099344+62723136 \[Beta]^2+73905397 \[Beta]^4)+\[Alpha]^3 (7967232+76268480 \[Beta]^2-182696832 \[Beta]^4-90084500 \[Beta]^6)-4 \[Alpha]^2 \[Beta] (2708608-19067120 \[Beta]^2-31361568 \[Beta]^4+15602721 \[Beta]^6)+\[Alpha] (403200-10834432 \[Beta]^2-58321312 \[Beta]^4+50938752 \[Beta]^6+8524395 \[Beta]^8)))