On the elegance of Ramanujan's series for π

2021/04/26 by Chieh-Lei Wong, Wong, Chieh-Lei · 1 voice
Chemistry · Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Molecular spectroscopy and chirality #math.NT

paper · pdf · doi:10.48550/arxiv.2104.12412

openalex publication_date 2021/04/26 · openalex created_date 2021/05/10 · openalex updated_date 2026/07/28

Abstract

Re presenting the traditional proof of Srinivasa Ramanujan's own favorite series for the reciprocal of π :\frac1π = (√(8))/(9801) ∑_n=0^+∞ ((4n)!)/((n!)⁴) \frac1103 + 26390n396⁴ⁿ ,as well as several other examples of Ramanujan's infinite series. As a matter of fact, the derivation of such formulae has involved specialized knowledge of identities of classical functions and modular functions.

Discussions

• His next most known discovery is a series for 1/pi that converges crazy fast, and looks absolutely horrific. He really had an intuitive brilliance that is extremely rare. arxiv.org/pdf/2104.12412 [bsky, 9 points, 1 comments]

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