Multisection method and further formulae for \(\pi\)
type: Item
instance of: scholarly article
title: Multisection method and further formulae for \(\pi\)
zbMATH Open document ID: 1170.11045
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2008-07-11T00:00:00Z
review text: The author considers an elementary approach for deriving infinite series expression of~\(\pi\) in the form \[ \sum_{n=0}^\infty\frac{P_m(n)\alpha^n}{\binom{2mn}{mn}}, \] where \(\alpha\)~is a rational number and \(P_m(n)\)~a polynomial of degree \(m\) in~\(n\); the cases covered include \(m=4,8,12,16,24\) with the announced possibility to extend the argument to~\(m\) being an arbitrary positive power of~2. A systematic search and proof of such identities was done previously in [\textit{G.~Almkvist, C.~Krattenthaler}, and \textit{J.~Petersson}, Exp. Math. 12, No. 4, 441--456 (2003; Zbl 1161.11419)].
reviewed by: Wadim Zudilin
Mathematics Subject Classification ID: 11Y60
Mathematics Subject Classification ID: 11B65
Mathematics Subject Classification ID: 65B10
zbMATH DE Number: 5300047
zbMATH Keywords: formula for \(\pi\)
zbMATH Keywords: binomial sum
zbMATH Keywords: central binomial coefficient
author: Deyin Zheng
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5300047