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Hypergeometric Differential Equation and New Identities for the Coefficients of Nørlund and Bühring
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Hypergeometric Differential Equation and New Identities for the Coefficients of Nørlund and Bühring
Інший ID:
2010 Mathematics Subject Classification: 33C20; 33C60; 34M35
DOI:10.3842/SIGMA.2016.052
DOI:10.3842/SIGMA.2016.052
Посилання:
Hypergeometric Differential Equation and New Identities for the Coefficients of Nørlund and Bühring / D. Karp, E. Prilepkina // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 44 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications.
The full collection is available at http://www.emis.de/journals/SIGMA/OPSFA2015.html.
This work has been supported by the Russian Science Foundation under project 14-11-00022.
We are also indebted to anonymous referees for a number of useful remarks that helped to
improve the exposition.
Дата:
2016
Переглядів:
539
Завантажень:
292
Анотація:
The fundamental set of solutions of the generalized hypergeometric differential equation in the neighborhood of unity has been built by Nørlund in 1955. The behavior of the generalized hypergeometric function in the neighborhood of unity has been described in the beginning of 1990s by Bühring, Srivastava and Saigo. In the first part of this paper we review their results rewriting them in terms of Meijer's G-function and explaining the interconnections between them. In the second part we present new formulas and identities for the coefficients that appear in the expansions of Meijer's G-function and generalized hypergeometric function around unity. Particular cases of these identities include known and new relations for Thomae's hypergeometric function and forgotten Hermite's identity for the sine function.
