Certain Integrals Arising from Ramanujan's Notebooks
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Certain Integrals Arising from Ramanujan's Notebooks
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| Creator |
Berndt, B.C.
Straub, A. |
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| Description |
In his third notebook, Ramanujan claims the specific. In a following cryptic line, which only became visible in a recent reproduction of Ramanujan's notebooks, Ramanujan indicates that a similar relation exists if logx were replaced by log²x in the first integral and logx were inserted in the integrand of the second integral. One of the goals of the present paper is to prove this claim by contour integration. We further establish general theorems similarly relating large classes of infinite integrals and illustrate these by several examples.
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| Date |
2019-02-13T17:39:21Z
2019-02-13T17:39:21Z 2015 |
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| Type |
Article
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| Identifier |
Certain Integrals Arising from Ramanujan's Notebooks / B.C. Berndt, A. Straub // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 5 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 33E20 DOI:10.3842/SIGMA.2015.083 http://dspace.nbuv.gov.ua/handle/123456789/147147 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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