S. I. Bezrodnykh, “Jacobi-Type Differential Relations for the Lauricella Function $F_D^{(N)}$”, Mat. Zametki, 99:6 (2016), 832–847; Math. Notes, 99:6 (2016), 821

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Matematicheskie Zametki, 2016, Volume 99, Issue 6, Pages 832–847
DOI: https://doi.org/10.4213/mzm11067 (Mi mzm11067)

This article is cited in 4 scientific papers (total in 4 papers)

Jacobi-Type Differential Relations for the Lauricella Function

F_{D}^{(N)}

$F_D^{(N)}$

S. I. Bezrodnykh^abc

^a Peoples Friendship University of Russia, Moscow
^b Federal Research Center "Computer Science and Control" of Russian Academy of Sciences
^c Lomonosov Moscow State University, P. K. Sternberg Astronomical Institute

Full-text PDF (588 kB) Citations (4)

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DOI: https://doi.org/10.4213/mzm11067

Abstract: For the generalized Lauricella hypergeometric function

F_{D}^{(N)}

$F_D^{(N)}$ , Jacobi-type differential relations are obtained and their proof is given. A new system of partial differential equations for the function

F_{D}^{(N)}

$F_D^{(N)}$ is derived. Relations between associated Lauricella functions are presented. These results possess a wide range of applications, including the theory of Riemann–Hilbert boundary-value problem.

Keywords: generalized Lauricella hypergeometric function, Jacobi-type differential relation, Jacobi identity, Gauss function, Christoffel–Schwarz integral.

Funding agency	Grant number
Russian Foundation for Basic Research	16-01-00781 16-07-01195
Russian Academy of Sciences - Federal Agency for Scientific Organizations
This work was supported by the Russian Foundation for Basic Research under grants 16-01-00781 and 16-07-01195 and by the program of the Russian Academy of Sciences “Contemporary problems of Theoretical Mathematics” (project “Optimal algorithms for the solution of problems of mathematical physics”).

Received: 19.01.2016

English version:
Mathematical Notes, 2016, Volume 99, Issue 6, Pages 821–833
DOI: https://doi.org/10.1134/S0001434616050205

Bibliographic databases:

Document Type: Article

UDC: 517

Language: Russian

Citation: S. I. Bezrodnykh, “Jacobi-Type Differential Relations for the Lauricella Function

F_{D}^{(N)}

$F_D^{(N)}$ ”, Mat. Zametki, 99:6 (2016), 832–847; Math. Notes, 99:6 (2016), 821–833

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm11067

https://doi.org/10.4213/mzm11067

https://www.mathnet.ru/eng/mzm/v99/i6/p832

This publication is cited in the following 4 articles:

A. Hasanov, T. K. Yuldashev, “Analytic Continuation Formulas for the Hypergeometric Functions in Three Variables of Second Order”, Lobachevskii J Math, 43:2 (2022), 386
S. I. Bezrodnykh, “The Lauricella hypergeometric function $F_D^{(N)}$, the Riemann–Hilbert problem, and some applications”, Russian Math. Surveys, 73:6 (2018), 941–1031
S. I. Bezrodnykh, “Finding the Coefficients in the New Representation of the Solution of the Riemann–Hilbert Problem Using the Lauricella Function”, Math. Notes, 101:5 (2017), 759–777
S. I. Bezrodnykh, V. I. Vlasov, “On a New Representation for the Solution of the Riemann–Hilbert Problem”, Math. Notes, 99:6 (2016), 932–937

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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