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 |