Related papers: Decomposition formulas associated with the multiva…
With the help of some techniques based on certain inverse pairs of symbolic operators, the authors investigated several decomposition formulas associated with Srivastava's Hypergeometric functions of three variables. Some operator…
By making use of some techniques based upon certain inverse new pairs of symbolic operators, the author investigate several decomposition formulas associated with Humbert hypergeometric functions $\Phi_1 $, $\Phi_2 $, $\Phi_3 $, $\Psi_1 $,…
The two most commonly used hypergeometric functions are the confluent hypergeometric function and the Gauss hypergeometric function. We review the available techniques for accurate, fast, and reliable computation of these two hypergeometric…
By making use of some techniques based upon certain inverse new pairs of symbolic operators, the author investigate several decomposition formulas associated with Lauricella's hypergeometric functions $F_A^{(r)}, F_B^{(r)}, F_C^{(r)}$ and…
Fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients were constructed recently. These fundamental solutions are directly connected with multiple Lauricella hypergeometric function 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…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
Decomposition formulas associated with the Lauricella multivariable hypergeometric functions were known, however, due to the recurrence of those formulas, additional difficulties may arise in the applications. Further study of the…
Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…
Mathematical functions, which often appear in mathematical analysis, are referred to as special functions and have been studied over hundreds of years. Many books and dictionaries are available that describe their properties and serve as a…
This paper gives a geometric description of functional spaces related to Domain Decomposition techniques for computing solutions of Laplace and Helmholtz equations. Understanding the geometric structure of these spaces leads to algorithms…
For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…
Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…
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…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
We are going to study properties of "hypergeometrization" -- an operator which act on analytic functions near the origin by inserting two Pochhammer symbols into their Taylor series. In essence, this operator maps elementary function into…
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…
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…
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,…