Related papers: A note on the generalized-hypergeometric solutions…
I consider the power series expansion of Lame function in the Weierstrass's form and its integral forms applying three term recurrence formula[1]. I investigate asymptotic expansions of Lame function for the cases of infinite series and…
The main result of the present paper is the construction of fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients. These fundamental solutions are directly connected with multiple…
Sequences that are defined by multisums of hypergeometric terms with compact support occur frequently in enumeration problems of combinatorics, algebraic geometry and perturbative quantum field theory. The standard recipe to study the…
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…
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…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
Six families of generalized hypergeometric series in a variable $x$ and an arbitrary number of parameters are considered. Each of them is indexed by an integer $n$. Linear recurrence relations in $n$ relate these functions and their product…
We continue the study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we show the following results: Theorem A: The multiple…
We briefly sketch a proof concerning the structure of the all-order epsilon-expansions of generalized hypergeometric functions with special sets of parameters.
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…
It is shown that the Confluent Heun Equation (CHEq) reduces for certain conditions of the parameters to a particular class of Quasi-Exactly Solvable models, associated with the Lie algebra $sl (2,{\mathbb R})$. As a consequence it is…
This paper explores the calculus of dual-valued functions and investigates the gamma function, beta function and generalized hypergeometric functions by incorporating dual numbers as parameters and variables. We examine its fundamental…
We apply solutions of Heun's general equation to the stationary Schr\"odinger equation with two quasi-exactly solvable elliptic potentials which depend on a real parameter $\ell$. We get finite-series solutions from power series expansions…
This article deals with two classes of quasi-exactly solvable (QES) trigonometric potentials for which the one-dimensional Schroedinger equation reduces to a confluent Heun equation (CHE) where the independent variable takes only finite…
Recent progress in analytical calculation of the multiple [inverse, binomial, harmonic] sums, related with epsilon-expansion of the hypergeometric function of one variable are discussed.
We solve connection problem between fundamental solutions at singular points $0$ and $1$ for the generalized hypergeometric function, using analytic continuation of the integral representation. All connection coefficients are products of…
It is shown that the regular-at-infinity solution of the 1D Schrodinger equation with the hyperbolic Poschl-Teller (h-PT) potential with integer parameters is expressible in terms of a n-order Heun polynomial in y=thr at an arbitrary…
We present some recent progresses on Heun functions, gathering results from classical analysis up to elliptic functions. We describe Picard's generalization of Floquet's theory for differential equations with doubly periodic coefficients…
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…
Hypergeometric equations with a dihedral monodromy group can be solved in terms of elementary functions. This paper gives explicit general expressions for quadratic monodromy invariants for these hypergeometric equations, using a…