Related papers: HYPERgeometric functions DIfferential REduction: M…

Recently, there emerges different versions of beta function and hypergeometric functions containing extra parameters. Gaining enlightenment from these ideas, we will first introduce a new extension of generalized hypergeometric function and…

Trager's Hermite reduction solves the integration problem for algebraic functions via integral bases. A generalization of this algorithm to D-finite functions has so far been limited to the Fuchsian case. In the present paper, we remove…

Geometric programming problem is a powerful tool for solving some special type non-linear programming problems. It has a wide range of applications in optimization and engineering for solving some complex optimization problems. Many…

The paper classifies algebraic transformations of Gauss hypergeometric functions with the local exponent differences $(1/2,1/4,1/4)$, $(1/2,1/3,1/6)$ and $(1/3,1/3,1/3)$. These form a special class of algebraic transformations of Gauss…

This paper, pursuing the work started in [10] and [11], holds six new formulae for {\pi}, see equations, through ratios of first kind elliptic integrals and some values of hypergeometric functions of three or four variables of Lauricella…

This note is devoted to the study of the links between the Hilbert function of a subscheme X of the projective space, and its geometric properties. We will assume that X is arithmetically Cohen-Macaulay, which allows us to characterize its…

In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…

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.

We describe the InfraRed Data Reduction (IRDR) software package, a small ANSI C library of fast image processing routines for automated pipeline reduction of infrared (dithered) observations. We developed the software to satisfy certain…

In this paper we consider basic hypergeometric functions introduced by Heine. We study mapping properties of certain ratios of basic hypergeometric functions having shifted parameters and show that they map the domains of analyticity onto…

We provide a set of diagonals of simple rational functions of three and four variables that are squares of Heun functions. These Heun functions obtained through creative telescoping, turn out to be either pullbacked $_2F_1$ hypergeometric…

Just as with the Gauss hypergeometric function, particular cases of the local Heun function can be Liouvillian (that is, "elementary") functions. One way to obtain these functions is by pull-back transformations of Gauss hypergeometric…

In this paper, we build on the work of [T. Hughes, G. Sangalli, VARIATIONAL MULTISCALE ANALYSIS: THE FINE-SCALE GREENS' FUNCTION, PROJECTION, OPTIMIZATION, LOCALIZATION, AND STABILIZED METHODS, SIAM Journal of Numerical Analysis, 45(2),…

Holographic reduced representations (HRR) are based on superpositions of convolution-bound $n$-tuples, but the $n$-tuples cannot be regarded as vectors since the formalism is basis dependent. This is why HRR cannot be associated with…

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…

Many applications in the sciences require numerically stable and computationally efficient evaluation of multivariate polynomials. Finding beneficial representations of polynomials, such as Horner factorisations, is therefore crucial.…

A new Hilbert-type integral inequality in the whole plane with the non-homogeneous kernel and parameters is given. The constant factor related to the hypergeometric function and the beta function is proved to be the best possible. As…

We introduce new hypergeometric series expansions of the solutions to the general Heun equation. The form of the Gauss hypergeometric functions used as expansion function differs from that used before. We derive three such expansions and…

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…

DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the…