Paris, R. B. A Kummer-type transformation for a \(_{2}F_{2}\) hypergeometric function. (English) Zbl 1062.33008 J. Comput. Appl. Math. 173, No. 2, 379-382 (2005). Summary: We obtain a Kummer-type transformation for the \(_{2}F_{2}(x)\) hypergeometric function with general parameters in the form of a sum of \(_{2}F_{2}(-x)\) functions. This result is specialised to the case where one pair of parameters differs by unity to generalize a recent result of A. R. Miller [J. Comput. Appl. Math. 157, 507–509 (2003; Zbl 1025.33003)]. Cited in 2 ReviewsCited in 20 Documents MSC: 33C20 Generalized hypergeometric series, \({}_pF_q\) Keywords:Generalized hypergeometric function; Kummer-type transformation Citations:Zbl 1025.33003 PDFBibTeX XMLCite \textit{R. B. Paris}, J. Comput. Appl. Math. 173, No. 2, 379--382 (2005; Zbl 1062.33008) Full Text: DOI Digital Library of Mathematical Functions: Cubic ‣ §16.6 Transformations of Variable ‣ Generalized Hypergeometric Functions ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function References: [1] Exton, H., On the reducibility of the Kampé de Fériet function, J. Comput. Appl. Math., 83, 119-121 (1997) · Zbl 0880.33012 [2] Miller, A. R., On a Kummer-type transformation for the generalized hypergeometric function \({}_2 F_2\), J. Comput. Appl. Math., 157, 507-509 (2003) · Zbl 1025.33003 [3] Paris, R. B.; Kaminski, D., Asymptotics and Mellin-Barnes Integrals (2001), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0983.41019 [4] Prudnikov, A. P.; Brychov, Y. A.; Marichev, O. I., Integrals and Series, Vol. 3 (1990), Gordon & Breach: Gordon & Breach Amsterdam [5] Slater, L. J., Confluent Hypergeometric Functions (1960), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0086.27502 [6] Slater, L. J., Generalized hypergeometric Functions (1966), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0135.28101 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.