Sofo, Anthony \(\pi\) and some other constants. (English) Zbl 1127.33003 JIPAM, J. Inequal. Pure Appl. Math. 6, No. 5, Paper No. 138, 14 p. (2005). The author considers a particular integral and reduces it to hypergeometric form. Using this result, some numerical constants including \(\pi\) are represented as Gauss hypergeometric series. These series have half integer parameters, for example \(_2F_1(7/2,7/2;9/2;1/2)\) (Example 3.3) and can therefore be evaluated (even at a generic point like \(_2F_1(7/2,7/2;8/2;x)\)).In principle such evaluations of Gauss hypergeometric series can be handled by an algorithm of Kelly Roach [Proc. ISSAC 1996, Zürich, 301–308 (1996; Zbl 0914.65009)]. Reviewer: Wolfram Koepf (Kassel) Cited in 8 Documents MSC: 33C05 Classical hypergeometric functions, \({}_2F_1\) 33B15 Gamma, beta and polygamma functions 11Y60 Evaluation of number-theoretic constants Keywords:hypergeometric summation; definite integration; binomial type series Citations:Zbl 0914.65009 PDFBibTeX XMLCite \textit{A. Sofo}, JIPAM, J. Inequal. Pure Appl. Math. 6, No. 5, Paper No. 138, 14 p. (2005; Zbl 1127.33003) Full Text: EuDML