Archiv der Mathematik

, Volume 99, Issue 2, pp 125–135 | Cite as

On a remarkable formula of Ramanujan



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.

Mathematics Subject Classification (2010)



Gamma function Fourier transforms 


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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Debraj Chakrabarti
    • 1
  • Gopala Krishna Srinivasan
    • 2
  1. 1.TIFR Centre for Applicable MathematicsChikkabommasandra, BengaluruIndia
  2. 2.Department of MathematicsIndian Institute of Technology BombayPowai, MumbaiIndia

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