Related papers: On digamma series convertible into hypergeometric …
Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…
We calculate some finite and infinite sums containing the digamma function in closed-form. For this purpose, we differentiate selected reduction formulas of the hypergeometric function with respect to the parameters applying some derivative…
In the last decades, the theory of digamma function has been developed with a high impact of interest by many authors. Here, we established some interesting results for digamma function, and also we have computed the values of digamma…
We consider the derivatives of Horn hypergeometric functions of any number variables with respect to their parameters. The derivative of the function in $n$ variables is expressed as a Horn hypergeometric series of $n+1$ infinite summations…
Hypergeometric structures in single and multiscale Feynman integrals emerge in a wide class of topologies. Using integration-by-parts relations, associated master or scalar integrals have to be calculated. For this purpose it appears useful…
The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is…
The Digamma and Polygamma functions are important tools in mathematical physics, not only for its many properties but also for the applications in statistical mechanics and stellar evolution. In many textbooks is found its develop almost by…
It is well-known that differentiation of hypergeometric function multiplied by a certain power function yields another hypergeometric function with a different set of parameters. Such differentiation identities for hypergeometric functions…
Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing…
We consider summations over digamma and polygamma functions, often with summands of the form (\pm 1)^n\psi(n+p/q)/n^r and (\pm 1)^n\psi^{(m)} (n+p/q)/n^r, where m, p, q, and r are positive integers. We develop novel general integral…
This paper considers various integrals where the integrand includes the log gamma function (or its derivative, the digamma function) multiplied by a trigonometric or hyperbolic function. Some apparently new integrals and series are…
Feynman integrals that have been evaluated in dimensional regularization can be written in terms of generalized hypergeometric functions. It is well known that properties of these functions are revealed in the framework of intersection…
In this paper, we give an algorithm to generate connection formulas of generalized hypergeometric functions ${}_p F_{p-1}$ for degenerated values of parameters. We also show that these connection formulas give a fast method for numerical…
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams.…
We systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided. As a byproduct new summation formulas…
As a generalization of Riemann-Liouville integral, we introduce integral transformations of convergent power series which can be applied to hypergeometric functions with several variables.
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
Results are presented for some infinite series appearing in Feynman diagram calculations, many of which are similar to the Euler series. These include both one-, two- and three-dimensional series. The sums of these series can be evaluated…
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 hypergeometric functions from the symmetries and other properties of…
Value of generalized hypergeometric function at a special point is calculated. More precisely, value of certain multiple integral over vanishing cycle (all arguments collapse to unity) is calculated. The answer is expressed in terms of…