An Integral Analogue of Theta Functions and Gauss Sums in Ramanujan's Lost Notebook
2009 ◽
Vol 147
(2)
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pp. 257-265
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Keyword(s):
AbstractOne page in Ramanujan's lost notebook is devoted to claims about a certain integral with two parameters. One claim gives an inversion formula for the integral that is similar to the transformation formula for theta functions. Other claims are remindful of Gauss sums. In this paper we prove all the claims made by Ramanujan about this integral.
Keyword(s):
2016 ◽
Vol 4
(3)
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pp. 1-20
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2010 ◽
Vol 117
(7)
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pp. 957-973
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2001 ◽
Vol 354
(2)
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pp. 705-733
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2012 ◽
Vol 64
(4)
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pp. 935-960
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A Transformation Formula Involving the Gamma and Riemann Zeta Functions in Ramanujan’s Lost Notebook
2010 ◽
pp. 199-210
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2006 ◽
Vol 316
(2)
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pp. 628-641
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1991 ◽
Vol 89
(1)
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pp. 60-105
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