Hypergeometric Differential Equation and New Identities for the Coefficients of Nørlund and Bühring
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, Sriva...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147748 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862530001385029632 |
|---|---|
| author | Karp, D. Prilepkina, E. |
| author_facet | Karp, D. Prilepkina, E. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-11-24T02:39:47Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147748 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T02:39:47Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Karp, D. Prilepkina, E. 2019-02-15T19:07:42Z 2019-02-15T19:07:42Z 2016 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. 1815-0659 2010 Mathematics Subject Classification: 33C20; 33C60; 34M35 DOI:10.3842/SIGMA.2016.052 https://nasplib.isofts.kiev.ua/handle/123456789/147748 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hypergeometric Differential Equation and New Identities for the Coefficients of Nørlund and Bühring Article published earlier |
| spellingShingle | Hypergeometric Differential Equation and New Identities for the Coefficients of Nørlund and Bühring Karp, D. Prilepkina, E. |
| title | Hypergeometric Differential Equation and New Identities for the Coefficients of Nørlund and Bühring |
| title_full | Hypergeometric Differential Equation and New Identities for the Coefficients of Nørlund and Bühring |
| title_fullStr | Hypergeometric Differential Equation and New Identities for the Coefficients of Nørlund and Bühring |
| title_full_unstemmed | Hypergeometric Differential Equation and New Identities for the Coefficients of Nørlund and Bühring |
| title_short | Hypergeometric Differential Equation and New Identities for the Coefficients of Nørlund and Bühring |
| title_sort | hypergeometric differential equation and new identities for the coefficients of nørlund and bühring |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147748 |
| work_keys_str_mv | AT karpd hypergeometricdifferentialequationandnewidentitiesforthecoefficientsofnørlundandbuhring AT prilepkinae hypergeometricdifferentialequationandnewidentitiesforthecoefficientsofnørlundandbuhring |