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Reduction and transformation formulas for the Appell and related functions in two variables
Author(s) -
Srivastava H. M.,
Shpot M. A.
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4289
Subject(s) - appell series , mathematics , hypergeometric function , bilateral hypergeometric series , lauricella hypergeometric series , generalized hypergeometric function , basic hypergeometric series , transformation (genetics) , reduction (mathematics) , hypergeometric function of a matrix argument , hypergeometric identity , hypergeometric distribution , ordinary differential equation , pure mathematics , function (biology) , simple (philosophy) , algebra over a field , differential equation , mathematical analysis , geometry , biochemistry , chemistry , philosophy , epistemology , evolutionary biology , biology , gene
In many seemingly diverse areas of applications, reduction, summation, and transformation formulas for various families of hypergeometric functions in one, two, and more variables are potentially useful, especially in situations when these hypergeometric functions are involved in solutions of mathematical, physical, and engineering problems that can be modeled by (for example) ordinary and partial differential equations. The main object of this article is to investigate a number of reductions and transformations for the Appell functions F 1 , F 2 , F 3 , and F 4 in two variables and the corresponding (substantially more general) double‐series identities. In particular, we observe that a certain reduction formula for the Appell function F 3 derived recently by Prajapati et al. , together with other related results, were obtained more than four decades earlier by Srivastava. We give a new simple derivation of the previously mentioned Srivastava's formula [Disp. Item 19. F3α,β,1,1;α+β;x,y=1x+y−xyx2F1(α,1;α+β;x)+y2F1(β,1;α+β;y), ...]. We also present a brief account of several other related results that are closely associated with the Appell and other higher‐order hypergeometric functions in two variables. Copyright © 2017 John Wiley & Sons, Ltd.