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A Kummer-type transformation for a \(_{2}F_{2}\) hypergeometric function. (English) Zbl 1062.33008

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)].

MSC:

33C20 Generalized hypergeometric series, \({}_pF_q\)

Citations:

Zbl 1025.33003
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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
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[6] Slater, L. J., Generalized hypergeometric Functions (1966), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0135.28101
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