Prove-n-0-a-n-b-n-c-n-n-c-c-a-b-c-a-c-b-Where-a-n-k-0-n-1-k-a-

Question Number 128321 by Dwaipayan Shikari last updated on 06/Jan/21

P r o v e

\underset{n ⩾ 0}{\sum^{\infty}} \frac{{(a)}_{n} {(b)}_{n}}{{(c)}_{n} n!} = \frac{Γ (c) Γ (c - a - b)}{Γ (c - a) Γ (c - b)}

W h e r e {(a)}_{n} = \underset{k = 0}{\prod^{n - 1}} (k + a)

Commented by Lordose last updated on 10/Jan/21

hypergeometric series

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