Class number three Ramanujan type series for 1/π
نویسندگان
چکیده
منابع مشابه
Domb’s Numbers and Ramanujan-sato Type Series for 1/π
In this article, we construct a general series for 1 π . We indicate that Ramanujan’s 1 π −series are all special cases of this general series and we end the paper with a new class of 1 π −series. Our work is motivated by series recently discovered by Takeshi Sato.
متن کاملA Matrix Form of Ramanujan-type Series for 1/π
In this paper we prove theorems related to the Ramanujan-type series for 1/π (type 3F2) and to the Ramanujan-like series, discovered by the author, for 1/π (type 5F4). Our developments for the cases 3F2 and 5F4 connect with the theory of modular functions and with the theory of CalabiYau differential equations, respectively.
متن کاملRamanujan Series for Arithmetical Functions
We give a short survey of old and new results in the theory of Ramanujan expansions for arithmetical functions.
متن کاملRamanujan Series Upside-down
We prove that there is a correspondence between Ramanujan-type formulas for 1/π and formulas for Dirichlet L-values. Our method also allows us to reduce certain values of the Epstein zeta function to rapidly converging hypergeometric functions. The Epstein zeta functions were previously studied by Glasser and Zucker.
متن کاملRamanujan-Sato-Like Series
Using the theory of Calabi–Yau differential equations we obtain all the parameters of Ramanujan–Sato-like series for 1/π2 as q-functions valid in the complex plane. Then we use these q-functions together with a conjecture to find new examples of series of non-hypergeometric type. To motivate our theory we begin with the simpler case of Ramanujan–Sato series for 1/π .
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1993
ISSN: 0377-0427
DOI: 10.1016/0377-0427(93)90302-r