3 papers
math.CA2026
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…
math.CA2026
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…
math.CA2025
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…