Ix(a,b)=Ix(a+n,b)+xa(1−x)b∑j=1nΓ(a+b+j−1)Γ(b)Γ(a+j)xj−1=Ix(a+n,b)+xa(1−x)ba∑j=0n−1(a+b)j−(a+1)j−xj