相关论文: A new integral solution of the hypergeometric equa…

A linearized version of Heisenberg's fundamental equation is quantized by path integral method.

We evaluate several classes of high weight hypergeometric series via Gamma, polylogarithm and elliptic integrals, mainly through distribution relations.

We find transformations of variables which preserve the form of the equation for the kernels of integral relations among solutions of the Heun equation. These transformations lead to new kernels for the Heun equation, given by single…

The exposition has been significantly altered, hopefully improved.

In this paper, we obtain new results related to Minkowski fractional integral inequality using generalized k-fractional integral operator which is in terms of the Gauss hypergeometric function.

In this paper we present a new first-order hyperbolic reformulation of the Cahn-Hilliard equation. The model is obtained from the combination of augmented Lagrangian techniques proposed earlier by the authors of this paper, with a classical…

We elaborate on the expansion of hypergeometric functions about rational parameters, where we focus mainly on the integer and half-integer case. The strategy and the basic steps of a recently developed algorithm for the expansion about…

Finite-part integration is a recently introduced method of evaluating convergent integrals by means of the finite part of divergent integrals [E.A. Galapon, {\it Proc. R. Soc. A 473, 20160567} (2017)]. Current application of the method…

This paper has been withdrawn by the authors.

Original English Summary. - A systematic method of constructing potentials, for which the one-variable Schroedinger equation can be solved in terms of the hypergeometric (HGM) function, is presented. All the potentials, obtained by…

In this paper, we obtain recursion formulas for the Kamp\'e de Fe\'riet hypergeometric matrix function. We also give finite and infinite summation formulas for the Kamp\'e de Fe\'riet hypergeometric matrix function.

Presented is a new method yielding parameterized solution to an interval parametric linear system. Some properties of this method are discussed. The solution enclosure it provides is compared to the enclosures by other methods. It is shown…

We aim to introduce a new extension of beta function and to study its important properties. Using this definition, we introduce and investigate new extended hypergeometric and confluent hypergeometric functions. Further, some hybrid…

The central idea of this article is to present a systematic approach to construct some recurrence relations for the solutions of the second-order linear difference equation of hypergeometric-type defined on the quadratic-type lattices. We…

The $q$-middle convolution was introduced by Sakai and Yamaguchi. In this paper, we reformulate $q$-integral transformations associated with the $q$-middle convolution. In particular, we discuss convergence of the $q$-integral…

We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.

A new multiple-integral representation of a general family of very-well-poised hypergeometric series is proved. Inspite of an analytic character of the result, it is motivated by the recent arithmetic progress for the values of the Riemann…

In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved.

This paper has been withdrawn because the content has been substantially improved in a later paper, arXiv:0806.1165.

This paper is devoted for the study of a new generalization of Struve function type. In this paper , We establish four new integral formulas involving the Galue type Struve function, which are express in term of the generalized (Wright)…