Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities
The main goal of this paper is to derive a number of identities for the generalized hypergeometric function evaluated at unity and for certain terminating multivariate hypergeometric functions from the symmetries and other properties of Meijer's function. For instance, we recover two- and thre...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211429 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities. Asena Çetinkaya, Dmitrii Karp and Elena Prilepkina. SIGMA 17 (2021), 098, 25 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862651452101492736 |
|---|---|
| author | Çetinkaya, Asena Karp, Dmitrii Prilepkina, Elena |
| author_facet | Çetinkaya, Asena Karp, Dmitrii Prilepkina, Elena |
| citation_txt | Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities. Asena Çetinkaya, Dmitrii Karp and Elena Prilepkina. SIGMA 17 (2021), 098, 25 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The main goal of this paper is to derive a number of identities for the generalized hypergeometric function evaluated at unity and for certain terminating multivariate hypergeometric functions from the symmetries and other properties of Meijer's function. For instance, we recover two- and three-term Thomae relations for ₃₂, give two- and three-term transformations for ₄₃ with one unit shift and ₅₄ with two unit shifts in the parameters, establish multi-term identities for general ₚₚ₋₁ and several transformations for terminating Kampé de Fériet and Srivastava ⁽³⁾ functions. We further present a presumably new formula for analytic continuation of ₚₚ₋₁(1) in parameters and reveal somewhat unexpected connections between the generalized hypergeometric functions and the generalized and ordinary Bernoulli polynomials. Finally, we exploit some recent duality relations for the generalized hypergeometric and -hypergeometric functions to derive multi-term relations for terminating series.
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| first_indexed | 2026-03-15T15:50:06Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211429 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T15:50:06Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Çetinkaya, Asena Karp, Dmitrii Prilepkina, Elena 2026-01-02T08:31:05Z 2021 Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities. Asena Çetinkaya, Dmitrii Karp and Elena Prilepkina. SIGMA 17 (2021), 098, 25 pages 1815-0659 2020 Mathematics Subject Classification: 33C20; 33C60; 33C70 arXiv:2105.05196 https://nasplib.isofts.kiev.ua/handle/123456789/211429 https://doi.org/10.3842/SIGMA.2021.098 The main goal of this paper is to derive a number of identities for the generalized hypergeometric function evaluated at unity and for certain terminating multivariate hypergeometric functions from the symmetries and other properties of Meijer's function. For instance, we recover two- and three-term Thomae relations for ₃₂, give two- and three-term transformations for ₄₃ with one unit shift and ₅₄ with two unit shifts in the parameters, establish multi-term identities for general ₚₚ₋₁ and several transformations for terminating Kampé de Fériet and Srivastava ⁽³⁾ functions. We further present a presumably new formula for analytic continuation of ₚₚ₋₁(1) in parameters and reveal somewhat unexpected connections between the generalized hypergeometric functions and the generalized and ordinary Bernoulli polynomials. Finally, we exploit some recent duality relations for the generalized hypergeometric and -hypergeometric functions to derive multi-term relations for terminating series. The second and the third-named authors have been supported by the Ministry of Science and Higher Education of the Russian Federation (agreement No. 075-02-2021-1395). The third-named author has also supported by RFBR (project 20-01-00018). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities Article published earlier |
| spellingShingle | Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities Çetinkaya, Asena Karp, Dmitrii Prilepkina, Elena |
| title | Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities |
| title_full | Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities |
| title_fullStr | Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities |
| title_full_unstemmed | Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities |
| title_short | Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities |
| title_sort | hypergeometric functions at unit argument: simple derivation of old and new identities |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211429 |
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