On four new mock theta functions
Bull. Korean Math. Soc.
Published online August 20, 2019
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 : 11F37
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