Abstract
Mock theta functions were first introduced by Ramanujan. Historically, mock theta functions can be represented as Eulerian forms, Appell-Lerch sums, Hecke-type double sums, and Fourier coefficients of meromorphic Jacobi forms. In this paper, in view of the q-Zeilberger algorithm and the Watson–Whipple transformation formula, we establish five three-parameter mock theta functions in Eulerian forms, and express them by Appell–Lerch sums. Especially, the main results generalize some two-parameter mock theta functions. For example, setting (m,q,x)→(1,q1/2,xq−1/2) in∑n=0∞(−q2;q2)nqn2+(2m−1)n(xqm,x−1qm;q2)n+1, we derive the universal mock theta function g2(x,q).
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