Formulas for Computing Euler-Type Integrals and Their Application to the Problem of Constructing a Conformal Mapping of Polygons

This paper deals with Euler-type integrals and the closely related Lauricella function , which is a hypergeometric function of many complex variables . For new analytic continuation formulas are found that represent it in the form of Horn hypergeometric series exponentially converging in correspondi...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics Vol. 63; no. 11; pp. 1955 - 1988
Main Author: Bezrodnykh, S. I.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.11.2023
Springer Nature B.V
Subjects:
Complex variables
Computation
Computational Mathematics and Numerical Analysis
Conformal mapping
Convergence
General Numerical Methods
Geometry
Hypergeometric functions
Hyperplanes
Identities
Integrals
Mathematics
Mathematics and Statistics
Partial differential equations
Polygons
Variables
analytic continuation
Schwarz–Christoffel integral
crowding effect
Lauricella and Horn functions
Euler-type hypergeometric integrals
ISSN:0965-5425, 1555-6662
Online Access:Get full text
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Summary:This paper deals with Euler-type integrals and the closely related Lauricella function , which is a hypergeometric function of many complex variables . For new analytic continuation formulas are found that represent it in the form of Horn hypergeometric series exponentially converging in corresponding subdomains of , including near hyperplanes of the form , , . The continuation formulas and identities for found in this paper make up an effective apparatus for computing this function and Euler-type integrals expressed in terms of it in the entire complex space , including complicated cases when the variables form one or several groups of closely spaced neighbors. The results are used to compute parameters of the Schwarz–Christoffel integral in the case of crowding and to construct conformal mappings of polygons.
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542523110052