Negative Binomial Series

Section 12.3 Negative Binomial Series

(a + b)^{- n} = \sum_{k = 0}^{\infty} (\binom{- n}{k}) a^{k} b^{- n - k}

(a + b)^{- n} = \sum_{k = 0}^{\infty} (- 1)^{k} (\binom{n + k - 1}{k}) a^{k} b^{- n - k}