1 citations · 1 across the 11 of their papers we have counts for
11 papers
Evaluation of terminating and non-terminating sums containing the digamma function
Sergei Kalmykov, Dmitrii Karp, Vinay Shukla
We derive transformation and summation formulas for terminating and nonterminating series involving the digamma function. Our principal results are obtained by a limiting process s…
On Askey's extension of Clausen's identity and its polynomial perturbation
Dmitrii Karp, Vinay Shukla
The celebrated Clausen's identity expresses the square of the Gauss hypergeometric series as a single hypergeometric series. Goursat showed in…
Polynomial perturbations of Euler's and Clausen's identities
Dmitrii Karp
A product of two hypergeometric series is generally not hypergeometric. However, there are a few cases when such product does reduce to a single hypergeometric series. The oldest r…
A new identity for the sum of products of generalized basic hypergeometric functions
S. I. Kalmykov, D. Karp, A. Kuznetsov
We prove a duality relation for generalized basic hypergeometric functions. It forms a -extension of a recent result of the second and the third named authors and generalizes bo…
Inequalities for some basic hypergeometric functions
S. I. Kalmykov, D. B. Karp
We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric function with respect simultaneous shi…
Log-concavity and Turán-type inequalities for the generalized hypergeometric function
S. I. Kalmykov, D. B. Karp
The paper studies logarithmic convexity and concavity of the generalized hypergeometric function with respect to simultaneous shift of several parameters. We use integral represent…