Related papers: Integral representation and functional inequalitie…
Several integrals involving powers and ordinary hypergeometric functions are rederived by means of a generalized hypergeometric function of two variables (Appell's function) recovering some well-known expressions as particular cases. Simple…
In this paper, a general form of integral inequalities of Hermite-Hadamard's type through differentiability for s-Convex function in second sense and whose all derivatives are absolutely continuous are established. The generalized integral…
We investigate Dirichlet-type series generated by representation functions that count the number of ways an integer can be expressed as a sum of 'k' signed higher even powers. By combining generalized theta generating functions with a…
Integral representations of hypergeometric functions proved to be a very useful tool for studying their properties. The purpose of this paper is twofold. First, we extend the known representations to arbitrary values of the parameters and…
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, that their monotonicity and convexity properties with respect…
In this paper, we first introduce certain forms of extended incomplete Pochhammer symbols which are then used to define families of extended incomplete generalized hypergeometric functions. For these functions, we investigate various…
In this paper we study the convergence of multiple Dirichlet L-series. In particular we give an integral representation of the series in the region of convergence by using Abel's summation formula. A certain generalized result is also…
We introduce and solve an infinite class of loop integrals which generalises the well-known ladder series. The integrals are described in terms of single-valued polylogarithmic functions which satisfy certain differential equations. The…
It is well known that finite-dimensional polyhedral convex sets can be generated by finitely many points and finitely many directions. Representation formulas in this spirit are obtained for convex polyhedra and generalized convex polyhedra…
Miller-Paris transformations are extensions of Euler's transformations for the Gauss hypergeometric functions to generalized hypergeometric functions of higher-order having integral parameter differences (IPD). In our recent work we…
Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain…
In this paper, we give the matrix version of Horn's hypergeometric function and its confluent cases. We also discuss the regions of convergence, the system of matrix differential equations of bilateral type, differential formulae and…
The purpose of this note is to provide an expository introduction to some more curious integral formulas and transformations involving generating functions. We seek to generalize these results and integral representations which effectively…
A generalization of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli--type polynomials. Related families of…
We describe the utility of integral representations for sums of basic hypergeometric functions. In particular we use these to derive an infinite sequence of transformations for symmetrizations over certain variables which the functions…
In this work we derive and evaluate some infinite integrals involving the product of a generalized logarithm and polynomial functions in the denominator. These integrals are expressed in terms of finite series involving the Hurwitz-Lerch…
We continue our study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we apply the approach of obtaining iteratated solutions to…
In this paper, a general integral identity for convex functions is derived. Then, we establish new some inequalities of the Simpson and the Hermite-Hadamard's type for functions whose absolute values of derivatives are convex. Some…
We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a four-fold, rational (Feynman-)parametric representation…
This paper addresses two primary objectives in the realm of classical multiple orthogonal polynomials with an arbitrary number of weights. Firstly, it establishes new and explicit hypergeometric expressions for type I Hahn multiple…