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A Partial Manuscript on Fourier and Laplace Transforms

In: Ramanujan's Lost Notebook

Author

Listed:
  • George E. Andrews

    (The Pennsylvania State University, Department of Mathematics)

  • Bruce C. Berndt

    (University of Illinois at Urbana-Champaign, Department of Mathematics)

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 $$\xi(s)\,and\,\Xi(s) $$

Suggested Citation

  • George E. Andrews & Bruce C. Berndt, 2013. "A Partial Manuscript on Fourier and Laplace Transforms," Springer Books, in: Ramanujan's Lost Notebook, edition 127, chapter 13, pages 285-305, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-4081-9_13
    DOI: 10.1007/978-1-4614-4081-9_13
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