A Partial Manuscript on Fourier and Laplace Transforms

George E. Andrews and Bruce C. Berndt
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George E. Andrews: The Pennsylvania State University, Department of Mathematics
Bruce C. Berndt: University of Illinois at Urbana-Champaign, Department of Mathematics

Chapter 13 in Ramanujan's Lost Notebook, 2013, pp 285-305 from Springer

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

Keywords: Zeta Function; Summation Formula; Riemann Zeta Function; Transformation Formula; Quarterly Report (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-4081-9_13

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DOI: 10.1007/978-1-4614-4081-9_13

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