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On the generalized Wright function. (English) Zbl 1027.33015

Summary: The paper is devoted to the study of the generalized Wright function. Conditions for the existence of \({_p\Psi_q}(z)\) are proved. The representation of the function in terms of the Mellin-Barnes integral and of the \(H\)-function are etablished. Special cases, involving the Mittag-Leffler function and its generalizations, are considered. The obtained results imply more precisely the known results.

MSC:

33E12 Mittag-Leffler functions and generalizations
33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
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