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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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