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A Partial Manuscript on Fourier and Laplace Transforms

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Ramanujan's Lost Notebook

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Abstract

Most of the results in the partial manuscript on integral transforms discussed in this chapter are classical. However, the partial manuscript contains one of the highlights of the book, a beautiful new transformation formula involving the logarithmic derivative of the gamma function. An extremely clever device used to prove this transformation formula harkens back to Ramanujan’s paper, New expressions for Riemann’s functions \(\xi(s)\,and\,\Xi(s) \)

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Notes

  1. 1.

    The authors are indebted to M.L. Glasser for the proof of this lemma. The authors’ original proof of this lemma was substantially longer than Glasser’s given here.

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Authors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, PA, USA

    George E. Andrews

  2. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Bruce C. Berndt

Authors
  1. George E. Andrews
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  2. Bruce C. Berndt
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Andrews, G.E., Berndt, B.C. (2013). A Partial Manuscript on Fourier and Laplace Transforms. In: Ramanujan's Lost Notebook. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4081-9_13

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