72 citations · 256 across the 31 of their papers we have counts for
30 papers · 1 filter
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…
Ratios of the Gauss hypergeometric functions with parameters shifted by integers: more on integral representations
Alexander Dyachenko, Dmitrii Karp
We consider the ratio of two Gauss hypergeometric functions, in which the parameters of the numerator function differ from the respective parameters of the denominator function by…
Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities
Asena Çetinkaya, Dmitrii Karp, Elena Prilepkina
The main goal of this paper is to derive a number of identities for the generalized hypergeometric function evaluated at unity and for certain terminating multivariate hypergeometr…
Transformations of the hypergeometric 4F3 with one unit shift: a group theoretic study
Dmitrii Karp, Elena Prilepkina
We study the group of transformations of 4F3 hypergeometric functions evaluated at unity with one unit shift in parameters. We reveal the general form of this family of transformat…
Completely monotonic ratios of basic and ordinary gamma functions
Christian Berg, Asena Cetinkaya, Dmitrii Karp
We investigate conditions for logarithmic complete monotonicity of product ratios of gamma and q-gamma functions whose arguments are linear functions of the variable. We give neces…
Further applications of the G function integral method
M. A. C. Candezano, D. B. Karp, E. G. Prilepkina
In our recent work we proposed a generalization of the beta integral method for derivation of the hypergeometric identities which can by analogy be termed "the G function integral…
Beyond the beta integral method: transformation formulas for hypergeometric functions via Meijer's G function
D. B. Karp, E. G. Prilepkina
The beta integral method proved itself as a simple nonetheless powerful method of generating hypergeometric identities at a fixed argument. In this paper we propose a generalizatio…
The Fox-Wright function near the singularity and branch cut
Dmitrii Karp, Elena Prilepkina
The Fox-Wright function is a further extension of the generalized hypergeometric function obtained by introducing arbitrary positive scaling factors into the arguments of the gamma…
A new identity for a sum of products of the generalized hypergeometric functions
Dmitrii Karp, Alexey Kuznetsov
Reduction formulas for sums of products of hypergeometric functions can be traced back to Euler. This topic has an intimate connection to summation and transformation formulas, con…
Uniformly convergent expansions for the generalized hypergeometric functions of the Bessel and Kummer types
Jose L. Lopez, Pedro J. Pagola, Dmitrii B. Karp
We derive a convergent expansion of the generalized hypergeometric function in terms of the Bessel functions that holds uniformly with respect to the argu…
Extensions of Karlsson-Minton summation theorem and some consequences of the first Miller-Paris transformation
Dmitrii B. Karp, Elena G. Prilepkina
In this paper we give several independent extensions of the Karlsson-Minton summation formula for the generalized hypergeometric function with integral parameters differences. In p…
Degenerate Miller-Paris transformations
Dmitrii B. Karp, Elena G. Prilepkina
Important new transformations for the generalized hypergeometric functions with integral parameter differences have been discovered some years ago by Miller and Paris and studied i…
Hypergeometric representations and differential-difference relations for some kernels appearing in mathematical physics
Dmitrii B. Karp, Yuri B. Melnikov, Irina V. Turuntaeva
The paper is an investigation of the analytic properties of a new class of special functions that appear in the kernels of a class of integral operators underlying the dynamics of…
New identities for a sum of products of the Kummer functions
S. I. Kalmykov, D. B. Karp
Recently, Feng, Kuznetsov and Yang discovered a very general reduction formula for a sum of products of the generalized hypergeometric functions (J. Math. Anal. Appl. 443(2016), 11…
Applications of the Stieltjes and Laplace transform representations of the hypergeometric functions
D. B. Karp, E. G. Prilepkina
In our previous work we found sufficient conditions to be imposed on the parameters of the generalized hypergeometric function in order that it be completely monotonic or of Stielt…
Hypergeometric Differential Equation and New Identities for the Coefficients of Nørlund and Bühring
Dmitrii Karp, Elena Prilepkina
The fundamental set of solutions of the generalized hypergeometric differential equation in the neighborhood of unity has been built by Nørlund in 1955. The behavior of the general…
Some new facts concerning the delta neutral H function of Fox
D. Karp, E. Prilepkina
In this paper we find several new properties of a class of Fox's H functions which we call delta neutral. In particular, we find an expansion in the neighborhood of finite nonzero…
Normalized incomplete beta function: log-concavity in parameters and other properties
Dmitrii Karp
The normalized incomplete beta function can be defined either as cumulative distribution function of beta density or as the Gauss hypergeometric function with one of the upper para…
Representations and inequalities for generalized hypergeometric functions
Dmitrii Karp
We find an integral representation for the generalized hypergeometric function unifying known representations via generalized Stieltjes, Laplace and cosine Fourier transforms. Usin…