On a remarkable formula of Ramanujan
Classical Analysis and ODEs
2012-06-25 v1 Complex Variables
Abstract
A simple proof of Ramanujan's formula for the Fourier transform of the square of the modulus of the Gamma function restricted to a vertical line in the right half-plane is given. The result is extended to vertical lines in the left half-plane by solving an inhomogeneous ODE. We then use it to calculate the jump across the imaginary axis.
Keywords
Cite
@article{arxiv.1206.5122,
title = {On a remarkable formula of Ramanujan},
author = {Debraj Chakrabarti and Gopala Krishna Srinivasan},
journal= {arXiv preprint arXiv:1206.5122},
year = {2012}
}
Comments
To appear in Archiv der Mathematik