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Some new identities for Ramanujan’s theta-function \(\phi(q)\) and applications. (English) Zbl 1210.33022
The author gives some new identities for Ramanujan’s theta-function \(\phi(q)\). They are used to defined a parameter \(A_n\) for any positive number \(n\) and find some new explicit values of ratios of \(\phi(q)\). In addition to these, the author proves a general formula for the explicit evaluations of the Ramanujan’s continued fraction \(c(q)\) at the special points \(q=e^{-\pi\sqrt{n}/2}\) and their special cases. The paper is well written.

MSC:
33E05 Elliptic functions and integrals
11A55 Continued fractions
11F20 Dedekind eta function, Dedekind sums
11F27 Theta series; Weil representation; theta correspondences
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