A solution of Sun's $520 challenge concerning 520/π

A solution of Sun's $520 challenge concerning 520/π
Mathew D. Rogers, Armin Straub — International Journal of Number Theory — Volume 9, Number 5, 2013, Pages 1273-1288


We prove a Ramanujan-type formula for 520/\(\pi\) conjectured by Sun. Our proof begins with a hypergeometric representation of the relevant double series, which relies on a recent generating function for Legendre polynomials by Wan and Zudilin. After showing that appropriate modular parameters can be introduced, we then apply standard techniques, going back to Ramanujan, for establishing series for 1/\(\pi\).


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    author = {Mathew D. Rogers and Armin Straub},
    title = {A solution of {S}un's \$520 challenge concerning $\frac{520}{\pi}$},
    journal = {International Journal of Number Theory},
    year = {2013},
    volume = {9},
    number = {5},
    pages = {1273--1288},
    doi = {10.1142/S1793042113500267},