Linear independent solutions and operational representations for hypergeometric functions of four variables

2014/01/21 by Maged G. Bin-Saad, Bin-Saad, Maged G., Anvar Hasanov +1
Mathematics · Physics and Astronomy · #33C20 #35A08 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.CA #math.MP #msc:33C20 #msc:35A08

paper · pdf · doi:10.48550/arxiv.1401.6928

8 pages

arxiv created 2014/01/21 · arxiv updated 2014/01/28

Abstract

In investigation of boundary-value problems for certain partial differential equations arising in applied mathematics, we often need to study the solution of system of partial differential equations satisfied by hypergeometric functions and find explicit linearly independent solutions for the system. Here we choose the Exton function K₂ among his 21 functions to show how to find the linearly independent solutions of partial differential equations satisfied by this function K₂. Based upon the classical derivative and integral operators we introduce a new operational images for hypergeometric function K₂. By means of these operational images a number of finite series and decomposition formulas are then fund.

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