On four new mock theta functions
Bull. Korean Math. Soc. 2020 Vol. 57, No. 2, 345-354
Published online August 20, 2019
Printed March 31, 2020
QiuXia Hu
Shanghai Normal University
Abstract : In this paper, we first give some representations for four new mock theta functions defined by Andrews \cite{Andrews} and Bringmann, Hikami and Lovejoy \cite{BHL} using divisor sums. Then, some transformation and summation formulae for these functions and corresponding bilateral series are derived as special cases of $_2\psi_2$ series \[\sum_{n=-\infty}^\infty\frac{(a,c;q)_n}{(b,d;q)_n}z^n\] and Ramanujan's sum \[\sum_{n=-\infty}^\infty\frac{(a;q)_n}{(b;q)_n}z^n.\]
Keywords : Mock theta functions, divisor sums, basic bilateral hypergeometric series
MSC numbers : 11F03, 11B65, 11F27
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