Fundamental solutions of generalized bi-axially symmetric Helmholtz equation

In this article for the generalized bi-axially symmetric Helmholz equation (GBSHE) in the domain four fundamental solutions expressed by confluent hypergeometric functions of Kummer of three variables are constructed in explicit form. By means of the expansion of the confluent hypergeometric functio...

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Bibliographic Details
Published inComplex variables and elliptic equations Vol. 52; no. 8; pp. 673 - 683
Main Author Hasanov, Anvar
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.08.2007
Subjects
AMS Subject Classifications
Confluent hypergeometric function
Expansion of hypergeometric function
Fundamental solutions
GBSHE
Logarithmic singularity
Primary 35A08
Singular partial differential equation
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ISSN1747-6933
1747-6941
DOI10.1080/17476930701300375

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Summary:In this article for the generalized bi-axially symmetric Helmholz equation (GBSHE) in the domain four fundamental solutions expressed by confluent hypergeometric functions of Kummer of three variables are constructed in explicit form. By means of the expansion of the confluent hypergeometric function it is proved that the solutions found have logarithmic singularities at r =  0 .
ISSN:1747-6933
1747-6941
DOI:10.1080/17476930701300375