Number Theory


Identities Inspired by the Ramanujan Notebooks, Second Series

Authors: Simon Plouffe

A series of formula is presented that are all inspired by the Ramanujan Notebooks [6]. One of them appears in the notebooks II which is for Zeta(3). That formula inspired others that appeared in 1998, 2006 and 2009 on the author’s website and later in literature [1][2][3]. New formulas for and the Catalan constant are presented along with a surprising series of approximations. A new set of identities is given for Eisenstein series. All of the formulas are conjectural since they were found experimentally. A new method is presented for the computation of the partition function. Une série de formules utilisant l’exponentielle est présentée. Ces résultats reprennent ceux apparaissant en 1998, 2006 et 2009 sur [1][2][3]. Elles sont toutes inspirées des Notebooks de Ramanujan tels que Zeta(3). Une nouvelle série pour Zeta(3) et la constante de Catalan sont présentés ainsi qu’une série d’approximations surprenantes. Une série d’identités nouvelles sont présentées concernant les séries d’Eisenstein. Toutes les formules présentées sont des conjectures, elles ont toutes été trouvées expérimentalement. Une nouvelle méthode est présentée pour le calcul des partages d’un entier.

Comments: 9 Pages.

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[v1] 2014-09-11 13:14:44

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