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http://dx.doi.org/10.4134/BKMS.b190236

ON FOUR NEW MOCK THETA FUNCTIONS  

Hu, QiuXia (Department of Mathematics Shanghai Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.57, no.2, 2020 , pp. 345-354 More about this Journal
Abstract
In this paper, we first give some representations for four new mock theta functions defined by Andrews [1] and Bringmann, Hikami and Lovejoy [5] using divisor sums. Then, some transformation and summation formulae for these functions and corresponding bilateral series are derived as special cases of 2𝜓2 series $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a,c;q)_n}{(b,d;q)_n}}z^n$$ and Ramanujan's sum $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a;q)_n}{(b;q)_n}}z^n$$.
Keywords
Mock theta functions; divisor sums; basic bilateral hypergeometric series;
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