Certain Integrals Arising from Ramanujan's Notebooks
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...
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| Date: | 2015 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2015
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/147147 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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