Inverse binomial series and a constant of Ramanujan
Résumé
In this article, we use a binomial transformation to link, through Bell's polynomials, certain "odd" harmonic series with the inverse binomial series studied by Kalmykov and Davydychev in relation with the Feynman diagrams. Surprisingly, this connection allows us to deduce some new and remarkable identities for the constant $C= \sum_{n\geq 1} \frac{1}{(2n)^3}(1+\frac13 + \dots + \frac{1}{2n-1})$ considered by S. Ramanujan in his notebooks.
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