Related papers: Summation formulas for Fox-Wright function
Using generalized hypergeometric functions to perform symbolic manipulation of equations is of great importance to pure and applied scientists. There are in the literature a great number of identities for the Meijer-G function. On the other…
This is a discussion of miscellaneous summation, integration and transformation formulas obtained using Fourier analysis. The topics covered are: Series of the form $\sum_{n\in\mathbb{Z}} c_ne^{\pi i \gamma n^2}$; Fusion of integrals, and…
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…
After reviewing some fundamental facts from the theory of theta hypergeometric series we derive, using indefinite summation, several summation, transformation, and expansion formulas for multibasic theta hypergeometric series. Some of the…
The Wright function, which arises in the theory of the space-time fractional diffusion equation, is an interesting mathematical object which has diverse connections with other special and elementary functions. The Wright function provides a…
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 prove a summation formula for a bilateral series whose terms are products of two basic hypergeometric functions. In special cases, series of this type arise as matrix elements of quantum group representations.
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…
A master formula of transformation formulas for bilinear sums of basic hypergeometric series is proposed. It is obtained from the author's previous results on a transformation formula for Milne's multivariate generalization of basic…
By some hypergeometric summation theorems, the authors establish a series of new infinite summation formulas involving generalized harmonic numbers related to Riemann-Zeta function, with three different patterns.
In this paper a natural generalization of the familiar H -function of Fox namely the I -function is proposed. Convergence conditions, various series representations, elementary properties and special cases for the I -function have also been…
New duality transformation formulas are proposed for multiple elliptic hypergeometric series of type $BC$ and of type $C$. Various transformation and summation formulas are derived as special cases to recover some previously known results.
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…
From the algebraic solution of $x^{n}-x+t=0$ for $n=2,3,4$ and the corresponding solution in terms of hypergeometric functions, we obtain a set of reduction formulas for hypergeometric functions. By differentiation and integration of these…
The $_{3}F_{2}$ hypergeometric function plays a very significant role in the theory of hypergeometric and generalized hypergeometric series. Despite that $_{3}F_{2}$ hypergeometric function has several applications in mathematics, also it…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
The Fibonacci number is the residue of a rational function, from which follows that Fibonacci number summation identities can be derived with the integral representation method, a method also used to derive combinatorial identities. A…
We introduce several new identities combining basic hypergeometric sums and integrals. Such identities appear in the context of superconformal index computations for three-dimensional supersymmetric dual theories. We give both analytic…
Some multiple hypergeometric transformation formulas arising from the balanced du- ality transformation formula are discussed through the symmetry. Derivations of some transformation formulas with different dimensions are given by taking…
The main object of this work is to show how some rather elementary techniques based upon certain inverse pairs of symbolic operators would lead us easily to several decomposition formulas associated with confluent hypergeometric functions…