Ramanujan-type formulae for 1/π: a second wind?

By Wadim Zudilin. 2006

66 citations recorded by the source corpus.

In 1914 S. Ramanujan recorded a list of 17 series for 1=…. 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 signiflcant events of the 20th century, in the opposite historical order. At flrst glance, the stories might be thought of a difierent nature.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/67903623a3f73f04ca6f1b6954989b9c65c9e1b7

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Citations in the corpus

On a q-deformation of modular forms (2018, background): “Bauer [7], is more than 150 years old but still attracts a lot of mathematical interest because of its belonging to a family of the so-called Ramanujan-type identities for 1/π (see [6, 10, 23, 26, 32] and, in particular, [3, Chap.”
Ramanujan-type supercongruences (2008, methodology): “(11) In Section 3 we present a (far from exhaustive) list of many other supercongruences which are analogues of the examples indicated in our recent mini-survey [14]; there one can find the analogue (31) of the formula for 1/π(3) experimentally discovered by 1A congruence modulo a prime p is said to”
Rational analogues of Ramanujan's series for 1/π† (2012, background): “See [23], [31] and [46] for some series for level 10 that were inspired by an example of Y.”
Eisenstein series and Ramanujan-type series for 1/π (2010, background): “D.V. Chudnovsky and G.V. Chudnovsky [27] independently proved several of Ramanujan’s series representations for 1/π and established new ones as well.”