Choi, Junesang Contiguous extensions of Dixon’s theorem on the sum of a \(_3F_2\). (English) Zbl 1185.33007 J. Inequal. Appl. 2010, Article ID 589618, 17 p. (2010). Summary: J. L. Lavoie, F. Grondin, A. K. Rathie and K. Arora [Math. Comput. 62, No. 205, 267–276 (1994; Zbl 0793.33006)] have succeeded in artificially constructing a formula consisting of twenty three interesting results, except for five cases, closely related to the classical Dixon’s theorem on the sum of a \(_3F_{2}\) by making a systematic use of some known relations among contiguous functions. We aim at presenting summation formulas for those five exceptional cases that can be derived by using the same technique developed by Bailey with the help of Gauss’s summation theorem and generalized Kummer’s theorem. Cited in 2 ReviewsCited in 2 Documents MSC: 33C20 Generalized hypergeometric series, \({}_pF_q\) Citations:Zbl 0793.33006 PDFBibTeX XMLCite \textit{J. Choi}, J. Inequal. Appl. 2010, Article ID 589618, 17 p. (2010; Zbl 1185.33007) Full Text: DOI References: [1] Rainville ED: Special Functions. The Macmillan, New York, NY, USA; 1960. · Zbl 0092.06503 [2] Srivastava HM, Choi J: Series Associated with the Zeta and Related Functions. Kluwer Academic Publishers, Dordrecht, The Netherlands; 2001. · Zbl 1014.33001 [3] Lavoie JL, Grondin F, Rathie AK, Arora K: Generalizations of Dixon’s theorem on the sum of a . Mathematics of Computation 1994, 62(205):267-276. · Zbl 0793.33006 [4] Kim YS, Rathie AK: On an extension formulas for the triple hypergeometric series due to Exton. Bulletin of the Korean Mathematical Society 2007, 44(4):743-751. 10.4134/BKMS.2007.44.4.743 · Zbl 1132.33313 [5] Lavoie JL, Grondin F, Rathie AK: Generalizations of Watson’s theorem on the sum of a . Indian Journal of Mathematics 1992, 34(2):23-32. · Zbl 0793.33005 [6] Lavoie JL, Grondin F, Rathie AK: Generalizations of Whipple’s theorem on the sum of a . Journal of Computational and Applied Mathematics 1996, 72(2):293-300. 10.1016/0377-0427(95)00279-0 · Zbl 0853.33005 [7] Bailey WN: Generalized Hypergeometric Series. Stechert-Hafner, New York, NY, USA; 1964. · Zbl 0011.02303 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.