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Some eighth order mock theta functions. (English) Zbl 1031.11007

Summary: 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.

MSC:

11B65 Binomial coefficients; factorials; \(q\)-identities
11F11 Holomorphic modular forms of integral weight
33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
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