Related papers: A note on some identities involving special functi…
Multiple elliptic polylogarithms can be written as (multiple) integrals of products of basic hypergeometric functions. The latter are computable, to arbitrary precision, using a q-difference equation and q-contiguous relations.
In this paper, we focus on clarifying the concept of solving equations of degree greater than six using continuous functions or hypergeometric functions and providing another proof of the non-existence of algebraic solutions for equations…
This paper shows that certain $\,_{3}F_{4}$ hypergeometric functions can be expanded in sums of pair products of $\,_{1}F_{2}$ functions. In special cases, the $\,_{3}F_{4}$ hypergeometric functions reduce to $\,_{2}F_{3}$ functions.…
General theory of elliptic hypergeometric series and integrals is outlined. Main attention is paid to the examples obeying properties of the "classical" special functions. In particular, an elliptic analogue of the Gauss hypergeometric…
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…
For zero-balanced Gaussian hypergeometric functions $ F(a,b;a+b;x),$ $a,b>0,$ we determine maximal regions of $ab$ plane where well-known Landen identities for the complete elliptic integral of the first kind turn on respective inequalities…
We give a definition of generalized hypergeometric functions over finite fields using modified Gauss sums, which enables us to find clear analogy with classical hypergeometric functions over the complex numbers. We study their fundamental…
This paper presents explicit algebraic transformations of some Gauss hypergeometric functions. Specifically, the transformations considered apply to hypergeometric solutions of hypergeometric differential equations with the local exponent…
We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.
In this article we present a method to implement orthogonal polynomials and many other special functions in Computer Algebra systems enabling the user to work with those functions appropriately, and in particular to verify different types…
The aim of this note is to provide a new identity connected with the Gauss hypergeometric function. This is achieved using results of certain combinatorial identities and a hypergeometric function approach.
The main result of the present paper is the construction of fundamental solutions for a class of multidimensional elliptic equations with three singular coefficients, which could be expressed in terms of a confluent hypergeometric function…
The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of…
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,…
We formulate and prove a combinatorial criterion to decide if an A-hypergeometric system of differential equations has a full set of algebraic solutions or not. This criterion generalises the so-called interlacing criterion in the case of…
We first show that hypergeometric functions appear naturally as spectral functions when applying pseudo-differential calculus to decipher heat kernel asymptotic in the situation where the symbol algebra is noncommutative. Such observation…
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…
In a joint paper [4] by Otsubo, Terasoma and the first author, we proved that the special value 3F2(a,b,q;a+b,q;1) of the generalized hypergeometric function is a linear combination of log of algebraic numbers if the triplet (a,b,q) of…
Recently found all the fundamental solutions of a multidimensional singular elliptic equation are expressed in terms of the well-known Lauricella hypergeometric function in many variables. In this paper, we find a unique solution of the…
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…