About a new kind of Ramanujan-type series. (English) Zbl 1083.33004

This paper obtains new types of formulas (of Ramanujan -type) for \(1/\pi ^2 \), and considers various other forms related to the theory of modular functions. Some other compact series summations are also investigated, and their relationships with several similar series summations are pointed out.


33C20 Generalized hypergeometric series, \({}_pF_q\)
11F99 Discontinuous groups and automorphic forms
33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)
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