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On some new mixed modular equations involving Ramanujan’s theta-functions. (English) Zbl 1488.33052

Summary: In his second notebook, Ramanujan recorded altogether 23 \(P\)-\(Q\) modular equations involving his theta functions. In this paper, we establish several new mixed modular equations involving Ramanujan’s theta-functions \(\varphi\) and \(\psi\) which are akin to those recorded in his notebook.

MSC:

33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
11A55 Continued fractions
11F27 Theta series; Weil representation; theta correspondences