a5=1;
a4=-5 s;
a3=(256-2304 \[Alpha]^2+1504 \[Alpha]^4-592 \[Alpha]^6+105 \[Alpha]^8-2560 \[Alpha] \[Beta]-1152 \[Alpha]^3 \[Beta]+672 \[Alpha]^5 \[Beta]-184 \[Alpha]^7 \[Beta]-1280 \[Beta]^2-1472 \[Alpha]^2 \[Beta]^2+16 \[Alpha]^4 \[Beta]^2-52 \[Alpha]^6 \[Beta]^2+384 \[Alpha] \[Beta]^3-64 \[Alpha]^3 \[Beta]^3+88 \[Alpha]^5 \[Beta]^3+736 \[Beta]^4+208 \[Alpha]^2 \[Beta]^4+198 \[Alpha]^4 \[Beta]^4-96 \[Alpha] \[Beta]^5-72 \[Alpha]^3 \[Beta]^5-144 \[Beta]^6-148 \[Alpha]^2 \[Beta]^6+40 \[Alpha] \[Beta]^7+25 \[Beta]^8)/(64 (-4 \[Alpha]+\[Alpha]^3-4 \[Beta]-\[Alpha]^2 \[Beta]-\[Alpha] \[Beta]^2+\[Beta]^3)^2);
a2=(-1280 \[Alpha]+2048 \[Alpha]^3-1184 \[Alpha]^5+224 \[Alpha]^7-25 \[Alpha]^9-1024 \[Beta]+768 \[Alpha]^2 \[Beta]+704 \[Alpha]^4 \[Beta]-496 \[Alpha]^6 \[Beta]+40 \[Alpha]^8 \[Beta]+512 \[Alpha] \[Beta]^2+832 \[Alpha]^3 \[Beta]^2+64 \[Alpha]^5 \[Beta]^2+4 \[Alpha]^7 \[Beta]^2+768 \[Beta]^3+512 \[Alpha]^2 \[Beta]^3+304 \[Alpha]^4 \[Beta]^3+24 \[Alpha]^6 \[Beta]^3-416 \[Alpha] \[Beta]^4+224 \[Alpha]^3 \[Beta]^4-86 \[Alpha]^5 \[Beta]^4-448 \[Beta]^5-400 \[Alpha]^2 \[Beta]^5+24 \[Alpha]^4 \[Beta]^5+4 \[Alpha]^3 \[Beta]^6+80 \[Beta]^7+40 \[Alpha]^2 \[Beta]^7-25 \[Alpha] \[Beta]^8)/(64 (-4 \[Alpha]+\[Alpha]^3-4 \[Beta]-\[Alpha]^2 \[Beta]-\[Alpha] \[Beta]^2+\[Beta]^3)^2);
a1=-(((16-8 \[Alpha]^2+5 \[Alpha]^4+16 \[Alpha] \[Beta]-4 \[Alpha]^3 \[Beta]-8 \[Beta]^2-2 \[Alpha]^2 \[Beta]^2-4 \[Alpha] \[Beta]^3+5 \[Beta]^4) (16-72 \[Alpha]^2+21 \[Alpha]^4-48 \[Alpha] \[Beta]-20 \[Alpha]^3 \[Beta]-8 \[Beta]^2-18 \[Alpha]^2 \[Beta]^2+12 \[Alpha] \[Beta]^3+5 \[Beta]^4))/(64 (-4 \[Alpha]+\[Alpha]^3-4 \[Beta]-\[Alpha]^2 \[Beta]-\[Alpha] \[Beta]^2+\[Beta]^3)^2));
a0=(256 \[Alpha]-256 \[Alpha]^3+224 \[Alpha]^5-80 \[Alpha]^7+25 \[Alpha]^9+256 \[Beta]-768 \[Alpha]^2 \[Beta]+608 \[Alpha]^4 \[Beta]-304 \[Alpha]^6 \[Beta]+65 \[Alpha]^8 \[Beta]+512 \[Alpha] \[Beta]^2-2880 \[Alpha]^3 \[Beta]^2+1552 \[Alpha]^5 \[Beta]^2-412 \[Alpha]^7 \[Beta]^2+25 \[Alpha]^9 \[Beta]^2+512 \[Beta]^3+704 \[Alpha]^2 \[Beta]^3-2192 \[Alpha]^4 \[Beta]^3+1012 \[Alpha]^6 \[Beta]^3-145 \[Alpha]^8 \[Beta]^3+1632 \[Alpha] \[Beta]^4+2128 \[Alpha]^3 \[Beta]^4-1522 \[Alpha]^5 \[Beta]^4+324 \[Alpha]^7 \[Beta]^4-288 \[Beta]^5+1584 \[Alpha]^2 \[Beta]^5+686 \[Alpha]^4 \[Beta]^5-308 \[Alpha]^6 \[Beta]^5-2064 \[Alpha] \[Beta]^6+916 \[Alpha]^3 \[Beta]^6+14 \[Alpha]^5 \[Beta]^6-624 \[Beta]^7-892 \[Alpha]^2 \[Beta]^7+210 \[Alpha]^4 \[Beta]^7-31 \[Alpha] \[Beta]^8-140 \[Alpha]^3 \[Beta]^8+153 \[Beta]^9-4 \[Alpha]^2 \[Beta]^9+33 \[Alpha] \[Beta]^10-9 \[Beta]^11)/(128 (-4 \[Alpha]+\[Alpha]^3-4 \[Beta]-\[Alpha]^2 \[Beta]-\[Alpha] \[Beta]^2+\[Beta]^3)^2);
S5\[Alpha]\[Beta][x_]=a0+a1 x+a2 x^2+a3 x^3+a4 x^4+a5 x^5;