Ramanujan type trigonometric formulae
نویسندگان
چکیده
منابع مشابه
Ramanujan-type formulae for 1/π: A second wind?∗
In 1914 S. Ramanujan recorded a list of 17 series for 1/π. We survey the methods of proofs of Ramanujan’s formulae and indicate recently discovered generalisations, some of which are not yet proven. Let us start with two significant events of the 20th century, in the opposite historical order. At first glance, the stories might be thought of a different nature. In 1978, R. Apéry showed the irra...
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In this paper we construct minimal cubature formulae of trigonometric degree: we obtain explicit formulae for low dimensions of arbitrary degree and for low degrees in all dimensions. A useful tool is a closed form expression for the reproducing kernels in two dimensions.
متن کامل1 9 M ay 2 00 8 Ramanujan - type formulae for 1 / π : A second wind ? ∗
In 1914 S. Ramanujan recorded a list of 17 series for 1/π. We survey the methods of proofs of Ramanujan’s formulae and indicate recently discovered generalizations, some of which are not yet proven. The twentieth century was full of mathematical discoveries. Here we expose two significant contributions from that time, in reverse chronological order. At first glance, the stories might be thought...
متن کاملRamanujan-type formulae and irrationality measures of some multiples of $\pi$
An explicit construction of simultaneous Padé approximations for generalized hypergeometric series and formulae for the quantities π √ d , d∈{1, 2, 3, 10005}, in terms of these series are used for estimates of irrationality measures of these multiples of π. Other possible applications are also discussed. Bibliography: 14 titles. Introduction An important role in the history of the Archimedes co...
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We present several supercongruences that may be viewed as p-adic analogues of Ramanujan-type series for 1/π and 1/π 2 , and prove three of these examples.
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ژورنال
عنوان ژورنال: Demonstratio Mathematica
سال: 2012
ISSN: 2391-4661
DOI: 10.1515/dema-2013-0418