first:

can you help me to integrate

[z^(q-1)]*[(1-z)^(p-1)]*{[(z^-(1/c))^(1/a)]^s}*{(Beta[z,q,p])^(j-1)}*{(Beta[1-z,p,q])^(n-j)} dz

where 0<z<1 and B[z,p,q] is the incomplete beta

Second

can we transform "Sum{[(p-1)! * (-1)^k * B[cq+ck-r/a , r/a +1] ] / k! * (p-1-k)!} from k=0 to k=infinity " to a hypergeomtric form ?

Any hints, suitable resources or and help is greatly appreciated.

Thank you in advance