On the Barnes double gamma function
We aim to achieve the following three goals. First of all, we collect all known definitions, transformation properties and functional identities of Barnes double gamma function . Second, we derive an algorithm for numerically computing the double gamma function and present its complete asymptotic ex...
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| Published in: | Integral transforms and special functions Vol. 34; no. 12; pp. 891 - 914 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Abingdon
Taylor & Francis
02-12-2023
Taylor & Francis Ltd |
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| Online Access: | Get full text |
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| Abstract | We aim to achieve the following three goals. First of all, we collect all known definitions, transformation properties and functional identities of Barnes double gamma function
. Second, we derive an algorithm for numerically computing the double gamma function and present its complete asymptotic expansion as
. Third, we derive some new properties, including a new product identity and new representations of the gamma modular forms
and
. |
|---|---|
| AbstractList | We aim to achieve the following three goals. First of all, we collect all known definitions, transformation properties and functional identities of Barnes double gamma function . Second, we derive an algorithm for numerically computing the double gamma function and present its complete asymptotic expansion as . Third, we derive some new properties, including a new product identity and new representations of the gamma modular forms and . We aim to achieve the following three goals. First of all, we collect all known definitions, transformation properties and functional identities of Barnes double gamma function . Second, we derive an algorithm for numerically computing the double gamma function and present its complete asymptotic expansion as . Third, we derive some new properties, including a new product identity and new representations of the gamma modular forms and . |
| Author | Alexanian, S. Kuznetsov, A. |
| Author_xml | – sequence: 1 givenname: S. surname: Alexanian fullname: Alexanian, S. organization: York University – sequence: 2 givenname: A. surname: Kuznetsov fullname: Kuznetsov, A. email: akuznets@yorku.ca organization: York University |
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| Cites_doi | 10.1088/0305-4470/34/36/320 10.1017/S0956792500001364 10.1137/0701008 10.1098/rsta.1901.0006 10.1007/s002200000261 10.2307/2048376 10.1112/plms/s1-31.1.358 10.1006/aima.2000.1946 10.1214/ECP.v14-1488 10.1016/j.cam.2022.114270 10.1016/j.jmaa.2017.08.043 10.1007/s10440-012-9718-y 10.1214/10-AOP577 10.1006/jath.2001.3578 10.3836/tjm/1270472992 10.1098/rspa.1997.0098 |
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| Copyright | 2023 Informa UK Limited, trading as Taylor & Francis Group 2023 2023 Informa UK Limited, trading as Taylor & Francis Group |
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| DOI | 10.1080/10652469.2023.2238115 |
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| References | Zwillinger D (e_1_3_3_13_1) 2007 e_1_3_3_7_1 e_1_3_3_6_1 e_1_3_3_9_1 e_1_3_3_8_1 e_1_3_3_18_1 e_1_3_3_17_1 e_1_3_3_19_1 e_1_3_3_14_1 e_1_3_3_16_1 e_1_3_3_15_1 e_1_3_3_3_1 e_1_3_3_10_1 e_1_3_3_2_1 e_1_3_3_5_1 e_1_3_3_12_1 e_1_3_3_4_1 e_1_3_3_11_1 |
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| Snippet | We aim to achieve the following three goals. First of all, we collect all known definitions, transformation properties and functional identities of Barnes... |
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| SubjectTerms | Algorithms asymptotic expansion Asymptotic series Barnes double gamma function Bernoulli numbers Gamma function Primary 33B15 Product differentiation Secondary 30E15 |
| Title | On the Barnes double gamma function |
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