Choi, Junesang; Rathie, Arjun K.; Purnima A note on Gauss’s second summation theorem for the series \(_2 F_1 (1/2)\). (English) Zbl 1168.33304 Commun. Korean Math. Soc. 22, No. 4, 509-512 (2007). Summary: We aim at deriving Gauss’s second summation theorem for the series \(_2 F_1 (1/2)\) by using Euler’s integral representation for \(_2F_1\). It seems that this method of proof has not been tried. Cited in 3 Documents MSC: 33C05 Classical hypergeometric functions, \({}_2F_1\) 33C20 Generalized hypergeometric series, \({}_pF_q\) 33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions) 33C70 Other hypergeometric functions and integrals in several variables 33C65 Appell, Horn and Lauricella functions Keywords:generalized hypergeometric series \(_p f_q\); Gauss’s second summation theorem for \(_2 F_1 (1/2)\); beta function PDFBibTeX XMLCite \textit{J. Choi} et al., Commun. Korean Math. Soc. 22, No. 4, 509--512 (2007; Zbl 1168.33304) Full Text: DOI