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 New series identities for $\frac{1}{\Pi}$ Commun. Korean Math. Soc. 2017 Vol. 32, No. 4, 865-874 https://doi.org/10.4134/CKMS.c160194Published online October 31, 2017 Mohammed M. Awad, Asmaa O. Mohammed, Medhat A. Rakha, Arjun K. Rathie Suez Canal University, Suez Canal University, Suez Canal University, Riverside Transit Campus 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 : hypergeometric summation theorems, Watson's theorem, Whipple's theorem, Ramanujan series for $\frac{1}{\pi}$ MSC numbers : 33C05, 33C20, 33C70 Downloads: Full-text PDF