Tuesday, 13 September 2016

summation - Compute a sum involving binomial coefficients

Let 0<a<b and p1>0 and p2>0 be integers. The question is to prove the following identity:



bj=a(jp1)(jp2)=p2q=0(1)q+1[(a+qp1+q+1)(ap2q)(b+1+qp1+q+1)(b+1p2q)]




Can this identity be generalised for p1,p2 being real?

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