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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.
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참고문헌 (29)
참고문헌 신청
A. K. Rathie / 2013 / On a special 3F2(1) and formulas for Ⅱ / Bull. Kerala Math. Assoc 10 (1) : 111 ~ 115
A. O. Mohammed / 2016 / On some series identities for 1-Ⅱ / J. Interpolat. Approx. Sci. Comput 2016 (2) : 105 ~ 109
A. P. Prudinkov / 1986 / Integrals and Series, Vol. 3 / Gordon and Brech Science
C. Wei / 2011 / Ⅱ formulae implied by two hypergeomtric series identity / arxive: 1110.6759.v1 [Math. C O] 31 Oct
C. Wei / 2012 / Ⅱ formulae with free parameters / J. Math. Anal. Appl 396 (2) : 880 ~ 887
A. O. Mohammed / 2016 / On some series identities for 1-Ⅱ / J. Interpolat. Approx. Sci. Comput 2016 (2) : 105 ~ 109
A. P. Prudinkov / 1986 / Integrals and Series, Vol. 3 / Gordon and Brech Science
C. Wei / 2011 / Ⅱ formulae implied by two hypergeomtric series identity / arxive: 1110.6759.v1 [Math. C O] 31 Oct
C. Wei / 2012 / Ⅱ formulae with free parameters / J. Math. Anal. Appl 396 (2) : 880 ~ 887
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