Integral Analogues of Theta Functions and Gauss Sums

  • George E. Andrews
  • Bruce C. Berndt


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.


Theta Function Transformation Formula Reciprocity Theorem Integral Analogue Foregoing Equality 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • George E. Andrews
    • 1
  • Bruce C. Berndt
    • 2
  1. 1.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA
  2. 2.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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