The Ramanujan Journal

, Volume 22, Issue 2, pp 221–230

Using Fourier–Legendre expansions to derive series for \(\frac{1}{\pi}\) and \(\frac{1}{\pi^{2}}\)

Article

DOI: 10.1007/s11139-010-9222-9

Cite this article as:
Levrie, P. Ramanujan J (2010) 22: 221. doi:10.1007/s11139-010-9222-9

Abstract

In this paper, we derive some series for \(\frac{1}{\pi}\) and \(\frac{1}{\pi^{2}}\) from the Fourier–Legendre expansions of odd powers of \(\sqrt{1-x^{2}}\).

Keywords

pi-series Fourier–Legendre series 

Mathematics Subject Classification (2000)

30B70 33B15 42C15 

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Applied EngineeringKarel de Grote-University CollegeHobokenBelgium
  2. 2.Department of Computer ScienceK.U.LeuvenHeverleeBelgium