Integral Analogues of Theta Functions and Gauss Sums

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 14 in Ramanujan's Lost Notebook, 2013, pp 307-327 from Springer

Abstract: Abstract This chapter is also related to two early papers on integrals, but all of the results are new. The integral examined by Ramanujan in this chapter satisfies a transformation formula similar to that satisfied by the classical theta functions. The integral can also be thought of as an analogue of Gauss sums or as an analogue of the classical Weierstrass σ-function.

Keywords: Theta Function; Transformation Formula; Reciprocity Theorem; Integral Analogue; Foregoing Equality (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-1-4614-4081-9_14

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