Related papers: A new integral solution of the hypergeometric equa…

This paper has been withdrawn, and is replaced with paper "Solvability of elliptic systems with square integrable boundary data" by the same authors.

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…

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.

This paper is an attempt to solve an important class of hypersingular integral equations of the second kind. To this end, we apply a new weighted and modified perturbation method which includes some special cases of the Adomian…

In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].

In this paper, we investigate the Euler-type integral representations for the generalized hypergeometric matrix function and develop some transformations in terms of hypergeometric matrix functions. Furthermore, unit and half arguments have…

We introduce two variants of $q$-hypergeometric equation. We obtain several explicit solutions of variants of $q$-hypergeometric equation. We show that a variant of $q$-hypergeometric equation can be obtained by a restriction of $q$-Appell…

In this article we prove a new elliptic hypergeometric integral identity. It previously appeared (as a conjecture) in articles by Rains, and Spiridonov and Vartanov. Moreover it gives a different proof of an identity in another article by…

This talk summarizes recent developments in the evaluation of Feynman integrals using hyperlogarithms. We discuss extensions of the original method, new results that were obtained with this approach and point out current problems and future…

We obtain special solutions of the $q$-Heun equation which are expressed as finite summations of $q$-hypergeometric functions. These solutions are obtained by considering the $q$-integral transformations of the polynomial-type solutions.

Withdrawn; replaced by longer, more detailed paper quant-ph/0010065.

Two integral solutions of q-difference equations of the hypergeometric type with |q|=1 are constructed by using the double sine function. One is an integral of the Barnes type and the other is of the Euler type.

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…

Several new identities for elliptic hypergeometric series are proved. Remarkably, some of these are elliptic analogues of identities for basic hypergeometric series that are balanced but not very-well-poised.

This paper has been withdrawn by the author. It will be replaced, substantially modified, by sections of the author's completed PhD thesis.

This paper is withdrawn.

This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite…

Young's integral inequality is complemented with an upper bound to the remainder. The new inequality turns out to be equivalent to Young's inequality, and the cases in which the equality holds become particularly transparent in the new…

This paper has been withdrawn by the authors. Significantly revised versions of the results of this paper are now available in arXiv:0707.0487v2 and arXiv:0808.3169v1.

This paper has been withdrawn.