Analogues of the general theta transformation formula

  title={Analogues of the general theta transformation formula},
  author={Atul Dixit},
  journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics},
  pages={371 - 399}
  • A. Dixit
  • Published 2013
  • Mathematics
  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics
A new class of integrals involving the confluent hypergeometric function 1F1(a;c;z) and the Riemann Ξ-function is considered. It generalizes a class containing some integrals of Ramanujan, Hardy and Ferrar and gives, as by-products, transformation formulae of the form F(z, α) = F(iz, β), where αβ = 1. As particular examples, we derive an extended version of the general theta transformation formula and generalizations of certain formulae of Ferrar and Hardy. A one-variable generalization of a… Expand
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