New series identities for 1 / π

Mohammed M. Awad, Asmaa O. Mohammed, Medhat A. Rakha, Arjun K. Rathie

Research output: Contribution to journalArticlepeer-review

Abstract

In the theory of hypergeometric and generalized hypergeometric series, classical summation theorems have been found interesting applications in obtaining various series identities for π, π2 and 1 / π. The aim of this research paper is to provide twelve general formulas for 1 / π. On specializing the parameters, a large number of very interesting series identities for 1 / π not previously appeared in the literature have been obtained. Also, several other results for multiples of π, π2, 1 π / 2, 1 π / 3 and 1 √ π have been obtained. The results are established with the help of the extensions of classical Gauss's summation theorem available in the literature.

Original languageEnglish
Pages (from-to)865-874
Number of pages10
JournalCommunications of the Korean Mathematical Society
Volume32
Issue number4
DOIs
Publication statusPublished - 2017
Externally publishedYes

Keywords

  • Hypergeometric summation theorems
  • Ramanujan series for 1 / π
  • Watson's theorem
  • Whipple's theorem

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this