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\(q\)-analogue of Wright function. (English) Zbl 1152.33312

Summary: We introduce a \(q\)-analogues of Wright function and its auxiliary functions as Barnes integral representations and series expansion. The relations between \(q\)-analogues of Wright function and some other functions are investigated.

MSC:

33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
33E12 Mittag-Leffler functions and generalizations
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References:

[1] G. E. Andrews, R. Askey, and R. Roy, Special Functions, vol. 71 of Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, UK, 1999. · Zbl 1129.33005
[2] I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. · Zbl 1129.33005
[3] G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, UK, 2nd edition, 2004. · Zbl 1129.33005
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