Barnes-Ismagilov Integrals and Hypergeometric Functions of the Complex Field
We examine a family ₚᶜq[⁽ᵃ⁾₍b₎; ] of integrals of Mellin-Barnes type over the space ℤ × ℝ, such that functions naturally arise in the representation theory of the Lorentz group. We express ₚᶜq() as quadratic expressions in the generalized hypergeometric functions ₚFq₋₁ and discuss further propertie...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210776 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Barnes-Ismagilov Integrals and Hypergeometric Functions of the Complex Field. Yury A. Neretin. SIGMA 16 (2020), 072, 20 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862600165327634432 |
|---|---|
| author | Neretin, Yury A. |
| author_facet | Neretin, Yury A. |
| citation_txt | Barnes-Ismagilov Integrals and Hypergeometric Functions of the Complex Field. Yury A. Neretin. SIGMA 16 (2020), 072, 20 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We examine a family ₚᶜq[⁽ᵃ⁾₍b₎; ] of integrals of Mellin-Barnes type over the space ℤ × ℝ, such that functions naturally arise in the representation theory of the Lorentz group. We express ₚᶜq() as quadratic expressions in the generalized hypergeometric functions ₚFq₋₁ and discuss further properties of the functions ₚᶜq().
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| first_indexed | 2026-03-14T02:17:53Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210776 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T02:17:53Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Neretin, Yury A. 2025-12-17T14:36:42Z 2020 Barnes-Ismagilov Integrals and Hypergeometric Functions of the Complex Field. Yury A. Neretin. SIGMA 16 (2020), 072, 20 pages 1815-0659 2020 Mathematics Subject Classification: 33C20;33C70;22E43 arXiv:1910.10686 https://nasplib.isofts.kiev.ua/handle/123456789/210776 https://doi.org/10.3842/SIGMA.2020.072 We examine a family ₚᶜq[⁽ᵃ⁾₍b₎; ] of integrals of Mellin-Barnes type over the space ℤ × ℝ, such that functions naturally arise in the representation theory of the Lorentz group. We express ₚᶜq() as quadratic expressions in the generalized hypergeometric functions ₚFq₋₁ and discuss further properties of the functions ₚᶜq(). The work was supported by the grant FWF, P31591. I am grateful to M.I. Graev, V.F. Molchanov, V.A. Spiridonov, and S.E. Derkachov for discussions and references. I also thank the referees for their useful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Barnes-Ismagilov Integrals and Hypergeometric Functions of the Complex Field Article published earlier |
| spellingShingle | Barnes-Ismagilov Integrals and Hypergeometric Functions of the Complex Field Neretin, Yury A. |
| title | Barnes-Ismagilov Integrals and Hypergeometric Functions of the Complex Field |
| title_full | Barnes-Ismagilov Integrals and Hypergeometric Functions of the Complex Field |
| title_fullStr | Barnes-Ismagilov Integrals and Hypergeometric Functions of the Complex Field |
| title_full_unstemmed | Barnes-Ismagilov Integrals and Hypergeometric Functions of the Complex Field |
| title_short | Barnes-Ismagilov Integrals and Hypergeometric Functions of the Complex Field |
| title_sort | barnes-ismagilov integrals and hypergeometric functions of the complex field |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210776 |
| work_keys_str_mv | AT neretinyurya barnesismagilovintegralsandhypergeometricfunctionsofthecomplexfield |