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<b>Fundamental solutions of generalized bi-axially symmetric Helmholtz equation</b>

Anvar HasanovInstitute of Mathematics, Uzbek Academy of Sciences , 29 F. Hodjaev Street, Tashkent 700125, Uzbekistan

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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.

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