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Milovanović, Gradimir V.; Rathie, Arjun K.

A new proof of a reduction formula for the Appell series \(F_3\) due to Bailey. (English) Zbl 1474.33061

Facta Univ., Ser. Math. Inf. 34, No. 5, 849-854 (2019).
Summary: In this short note, we provide a new proof of an interesting and useful reduction formula for the Appell series \(F_3\) due to W. N. Bailey [Q. J. Math., Oxf. II. Ser. 4, 237–240 (1953; Zbl 0051.30803)].

MSC:

33C65 Appell, Horn and Lauricella functions
33C15 Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)
33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)

Keywords:

Appell series; Humbert series; Whipple summation theorem; reduction formula; special functions

Citations:

Zbl 0051.30803
Cite Review PDF
Full Text: DOI

References:

[1] 1.G. E. Andrews, R. Askey, R. Roy:Special Functions. Cambridge University Press, Cambridge, 1999. · Zbl 0920.33001
[2] 2.P. Appell:Sur les fonctiones hyp´ergeometrques de plusieurs variables. M´em. Sc. Math., Fasc. III, Gauthier-Villars, Paris, 1925. · JFM 51.0281.09
[3] 3.W. N. Bailey:Generalized Hypergeometric Series. Cambridge University Press, Cambridge, 1935. · JFM 61.0406.01
[4] 4.W. N. Bailey:On the sum of a terminating3F2(1). Quart. J. Math. Oxford Ser. (2) 4(1953), 237-240. · Zbl 0051.30803
[5] 5.Yu. A. Brychkov, N. Saad:On some formulas for the Appell function F3(a, a′, b, b′;c;w, z). Integral Transf. Spec. Funct.26(11) (2015), 910-923. · Zbl 1331.33030
[6] 6.A. Erd´elyi, W. Magnus, F. Oberhettinger, F. G. Tricomi:Higher Transcendental Functions, Vol. 1. McGraw-Hill, New York, 1953. · Zbl 0051.30303
[7] 7.P. Humbert:Sur les fonctions hypercylindriques, Comptes Rendus de Sciences de l’Acad´emie des Sciences (Paris),171(1920), 490-492. · JFM 47.0348.01
[8] 8.G. V. Milovanovi´c:Numerical Analysis and Approximation Theory - Introduction to Numerical Processes and Solving Equations, Zavod za udzbenike, Beograd, 2014 (Serbian).
[9] 9.E. D. Rainville:Special Functions. The Macmillan Company, New York, 1960. · Zbl 0092.06503
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