Fundamental solutions of the generalized Helmholtz equation with several singular coefficients and confluent hypergeometric functions of many variables

DOI10.1134/S1995080220010047zbMath1450.35007arXiv1908.07158OpenAlexW3015788933MaRDI QIDQ2206996

Yanyan Li

Publication date: 27 October 2020

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.07158

zbMATH Keywords

confluent hypergeometric functionLauricella functionsdecomposition formula

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Appell, Horn and Lauricella functions (33C65)

Related Items (8)

Generalized solution of the Cauchy problem for hyperbolic equation with two lines of degeneracy of the second kind ⋮ Exact solutions of the thin beam with degrading hysteresis behavior ⋮ The Neumann problem for a multidimensional elliptic equation with several singular coefficients in an infinite domain ⋮ Dirichlet problem for the Laplace equation in the hyperoctant of a multidimensional ball ⋮ Potentials for three-dimensional singular elliptic equation and their application to the solving a mixed problem ⋮ Self-similar solutions of some model degenerate partial differential equations of the second, third, and fourth order ⋮ Потенциалы для трехмерного эллиптического уравнения с одним сингулярным коэффициентом и их применение ⋮ Holmgren's problem for the Laplace equation in the hyperoctant of a multidimensional ball

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On fundamental solutions for 3D singular elliptic equations with a parameter
• Solution of the spatial Tricomi problem for a singular mixed-type equation by the method of integral equations
• The Dirichlet problem for a 3D elliptic equation with two singular coefficients
• Fundamental solutions for a class of three-dimensional elliptic equations with singular coefficients
• On a boundary problem with Neumann's condition for 3D singular elliptic equations
• On fundamental solutions for multidimensional Helmholtz equation with three singular coefficients
• Spatial boundary problem with the Dirichlet-Neumann condition for a singular elliptic equation
• Decomposition formulas associated with the Lauricella multivariable hypergeometric functions
• Some decomposition formulas associated with the Lauricella function \(F_{A}^{(r)}\) and other multiple hypergeometric functions
• The Dirichlet problem for the generalized bi-axially symmetric Helmholtz equation
• ON AN ANALOGUE OF THE HOLMGREN'S PROBLEM FOR 3D SINGULAR ELLIPTIC EQUATION
• Fundamental solution of multidimensional axisymmetric Helmholtz equation
• Fundamental solutions of the bi-axially symmetric Helmholtz equation
• THE FOURTH DOUBLE-LAYER POTENTIAL FOR A GENERALIZED BI-AXIALLY SYMMETRIC HELMHOLTZ EQUATION
• CONFLUENT HYPERGEOMETRIC FUNCTIONS OF MANY VARIABLES AND THEIR APPLICATION TO THE FINDING OF FUNDAMENTAL SOLUTIONS OF THE GENERALIZED HELMHOLTZ EQUATION WITH SINGULAR COEFFICIENTS
• Third double-layer potential for a generalized bi-axially symmetric Helmholtz equation
• Double-layer potentials for a generalized bi-axially symmetric Helmholtz equation II
• Fundamental solutions of generalized bi-axially symmetric Helmholtz equation
• A solution of the Neumann–Dirichlet boundary value problem for generalized bi-axially symmetric Helmholtz equation
• EXPANSIONS OF APPELL'S DOUBLE HYPERGEOMETRIC FUNCTIONS

This page was built for publication: Fundamental solutions of the generalized Helmholtz equation with several singular coefficients and confluent hypergeometric functions of many variables