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arXiv · 1204.6569

Some extensions of Ramanujan's 1-psi-1 summation formula

N. M. Vildanov
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Abstract

We have found several summation formulas that extend Ramanujan's psi sum. First contains a parameter $α=1/N$, $N$ is a positive integer, and transforms to $q$-beta integral in the limit $N\to\infty$. The other is a $q$-analogue of generalized binomial theorem, expansion of $(1+t)^a$ in powers of $t^α$, $0<α\leq 1$, and it expresses the sum of a certain series in terms of a bibasic integral.

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N. M. Vildanov. 2012-04-30. Some extensions of Ramanujan's 1-psi-1 summation formula. https://arxiv.org/abs/1204.6569

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