Some Nice Sums are Almost as Nice if you turn them Upside Down

Details Some Nice Sums are Almost as Nice if you turn them Upside Down Some Nice Sums are Almost as Nice if you turn them Upside Down

2009-07-18

arxiv.org/abs/0907.3174v2

Mathematics

Combinatorics

6 pages

Scientific paper

We represent the sums $\sum_{k=0}^{n-1}{n \choose k}^{-2}$, $\sum_{k=0}^m{m\choose k}^{-1}{a\choose n-k}^{-1}$, $\sum_{k=0}^{n-1}\frac{q^{-k(k-1)}}{{\genfrac{[}{]}{0pt}{}{n}{k}}_q}$, and the sum of the reciprocals of the summands in Dixon's identity, each as a product of an {\it indefinite hypergeometric sum} times a (closed form) {\it hypergeometric sequence}

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