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NEW SERIES IDENTITIES FOR ${\frac{1}{\Pi}}$

  • Awad, Mohammed M. (Department of Mathematics Faculty of Science Suez Canal University) ;
  • Mohammed, Asmaa O. (Department of Mathematics Faculty of Science Suez Canal University) ;
  • Rakha, Medhat A. (Department of Mathematics Faculty of Science Suez Canal University) ;
  • Rathie, Arjun K. (Department of Mathematics School of Mathematical and Physical Sciences Central University of Kerala Riverside Transit Campus)
  • Received : 2016.09.20
  • Accepted : 2016.12.09
  • Published : 2017.10.31

Abstract

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

Keywords

References

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