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  • Journal of the London Mathematical Society, Volume 62, Issue 2
  • October 2000, pp. 321-335

SOME EIGHTH ORDER MOCK THETA FUNCTIONS

  • BASIL GORDON (a1) and RICHARD J. McINTOSH (a2)
  • Published online: 01 January 2001
Abstract

A method is developed for obtaining Ramanujan's mock theta functions from ordinary theta functions by performing certain operations on their q-series expansions. The method is then used to construct several new mock theta functions, including the first ones of eighth order. Summation and transformation formulae for basic hypergeometric series are used to prove that the new functions actually have the mock theta property. The modular transformation formulae for these functions are obtained.

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Journal of the London Mathematical Society
  • ISSN: 0024-6107
  • EISSN: 1469-7750
  • URL: /core/journals/journal-of-the-london-mathematical-society
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