72 citations · 256 across the 31 of their papers we have counts for
36 papers
A look at generalized trigonometric functions as functions of their two parameters and further new properties
Dmitrii Karp, Elena Prilepkina
Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, th…
Log-concavity and log-convexity of series containing multiple Pochhammer symbols
Dmitrii Karp, Yi Zhang
In this paper, we study power series with coefficients equal to a product of a generic sequence and an explicitly given function of a positive parameter expressible in terms of the…
On digamma series convertible into hypergeometric series
Asena Çetinkaya, Dmitrii Karp
Series containing the digamma function arise when calculating the parametric derivatives of the hypergeometric functions and play a role in evaluation of Feynman diagrams. As these…
Trigonometric identities: from Hermite via Meijer, Nørlund and Braaksma to Chu and Johnson and beyond
Alexander Dyachenko, Dmitrii Karp
Known already to the ancient Greeks, today trigonometric identities come in a large variety of tastes and flavours. In this large family there is a subfamily of interpolation-like…
Convergent expansions and bounds for the incomplete elliptic integral of the second kind near the logarithmic singularity
Dmitrii Karp, Yi Zhang
We find two series expansions for Legendre's second incomplete elliptic integral in terms of recursively computed elementary functions. Both expansions converge at every…
Hypergeometric with integral parameter differences
Dmitrii Karp, Elena Prilepkina
In this paper we continue investigation of the hypergeometric function as the function of its seven parameters. We deduce several reduction formulas for this function…