On a remarkable formula of Ramanujan

Debraj Chakrabarti; Gopala Krishna Srinivasan

doi:10.1007/s00013-012-0416-9

On a remarkable formula of Ramanujan

Debraj Chakrabarti, Gopala Krishna Srinivasan

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

A simple proof of Ramanujan's formula for the Fourier transform of {pipe}Γ (a + it){pipe} ² is given where a is fixed and has positive real part and t is real. The result is extended to other values of a by solving an inhomogeneous ODE, and we use it to calculate the jump across the imaginary axis.

Original language	English
Pages (from-to)	125-135
Number of pages	11
Journal	Archiv der Mathematik
Volume	99
Issue number	2
DOIs	https://doi.org/10.1007/s00013-012-0416-9
State	Published - Aug 2012

Keywords

Fourier transforms
Gamma function

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10.1007/s00013-012-0416-9

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title = "On a remarkable formula of Ramanujan",

abstract = "A simple proof of Ramanujan's formula for the Fourier transform of {pipe}Γ (a + it){pipe} 2 is given where a is fixed and has positive real part and t is real. The result is extended to other values of a by solving an inhomogeneous ODE, and we use it to calculate the jump across the imaginary axis.",

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AB - A simple proof of Ramanujan's formula for the Fourier transform of {pipe}Γ (a + it){pipe} 2 is given where a is fixed and has positive real part and t is real. The result is extended to other values of a by solving an inhomogeneous ODE, and we use it to calculate the jump across the imaginary axis.

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KW - Gamma function

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VL - 99

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JO - Archiv der Mathematik

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On a remarkable formula of Ramanujan

Abstract

Keywords

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