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

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Title: Formulas for Computing the Lauricella Function in the Case of Crowding of Variables.
Authors: Bezrodnykh, S. I.1 (AUTHOR) sbezrodnykh@mail.ru
Source: Computational Mathematics & Mathematical Physics. Dec2022, Vol. 62 Issue 12, p2069-2090. 22p.
Subjects: Functions of several complex variables, Intersection numbers, Hypergeometric functions, Hypergeometric series, Partial differential equations, Integral functions, Conformal mapping
Abstract: 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. [ABSTRACT FROM AUTHOR]
Copyright of Computational Mathematics & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Formulas for Computing the Lauricella Function in the Case of Crowding of Variables.
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  Data: <searchLink fieldCode="JN" term="%22Computational+Mathematics+%26+Mathematical+Physics%22">Computational Mathematics & Mathematical Physics</searchLink>. Dec2022, Vol. 62 Issue 12, p2069-2090. 22p.
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  Data: 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Computational Mathematics & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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