, Volume 194, Issue 1, pp 183-207

Legendre polynomials and Ramanujan-type series for 1/π

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Abstract

We resolve a family of recently observed identities involving 1/π using the theory of modular forms and hypergeometric series. In particular, we resort to a formula of Brafman which relates a generating function of the Legendre polynomials to a product of two Gaussian hypergeometric functions. Using our methods, we also derive some new Ramanujan-type series.

On Jon Borwein’s 60th birthday
The third author is supported by Australian Research Council grant DP110104419.