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On a remarkable formula of Ramanujan

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Abstract

A simple proof of Ramanujan’s formula for the Fourier transform of |Γ (a + it)|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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Authors and Affiliations

  1. TIFR Centre for Applicable Mathematics, Sharada Nagar, Chikkabommasandra, Bengaluru, 560065, India

    Debraj Chakrabarti

  2. Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

    Gopala Krishna Srinivasan

Authors
  1. Debraj Chakrabarti
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  2. Gopala Krishna Srinivasan
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Correspondence to Gopala Krishna Srinivasan.

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Chakrabarti, D., Srinivasan, G.K. On a remarkable formula of Ramanujan. Arch. Math. 99, 125–135 (2012). https://doi.org/10.1007/s00013-012-0416-9

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  • DOI: https://doi.org/10.1007/s00013-012-0416-9

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