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Some Eighth Order Mock Theta Functions
Author(s) -
Gordon Basil,
Mcintosh Richard J.
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610700008735
Subject(s) - ramanujan theta function , ramanujan's sum , theta function , mathematics , transformation (genetics) , basic hypergeometric series , hypergeometric function , pure mathematics , property (philosophy) , algebra over a field , order (exchange) , construct (python library) , computer science , biochemistry , chemistry , philosophy , epistemology , gene , programming language , finance , economics
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.