Formulas for Computing the Lauricella Function in the Case of Crowding of Variables

For the Lauricella function , which is a hypergeometric function of several complex variables , analytic continuation formulas are constructed that correspond to the intersection of an arbitrary number of singular hyperplanes of the form , , These formulas give an expression for the considered funct...

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Vydané v:Computational mathematics and mathematical physics Ročník 62; číslo 12; s. 2069 - 2090
Hlavný autor: Bezrodnykh, S. I.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Moscow Pleiades Publishing 01.12.2022
Springer Nature B.V
Predmet:
Complex variables
Computational Mathematics and Numerical Analysis
Conformal mapping
Hypergeometric functions
Hyperplanes
Mathematics
Mathematics and Statistics
Partial Differential Equations
analytic continuation
crowding effect
Lauricella and Horn functions
hypergeometric functions of several variables
ISSN:0965-5425, 1555-6662
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Popis
Shrnutí:For the Lauricella function , which is a hypergeometric function of several complex variables , analytic continuation formulas are constructed that correspond to the intersection of an arbitrary number of singular hyperplanes of the form , , These formulas give an expression for the considered function in the form of linear combinations of Horn hypergeometric series in variables satisfying the same system of partial differential equations as the original series defining in the unit polydisk. By applying these formulas, the function and Euler-type integrals expressed in terms of can be efficiently computed (with the help of exponentially convergent series) in the entire complex space in the complicated cases when the variables form one or several groups of “very close” quantities. This situation is referred to as crowding, with the term taken from works concerned with conformal maps.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542522120041