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On a remarkable formula of Ramanujan

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 Added by Debraj Chakrabarti
 Publication date 2012
  fields
and research's language is English




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A simple proof of Ramanujans 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.



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