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Generalized Wright function and its properties using extended beta function. (English) Zbl 1454.33004

Summary: Solving a linear partial differential equation witness a noteworthy role of Wright function. Due to its usefulness and various applications, a variety of its extentions (and generalizations) have been investigated and presented. The purpose and design of the paper is intended to study and come up with a new extention of the genralized Wright function by using generalized beta function and obtain some integral representation of the freshly defined function. Also we present the Mellin transform of this function in the form of Fox Wright function. Furthermore, we obtain the recurrence relation, derivative formula for the said function and also by using an extended Riemann-Liouville fractional derivative, we present a fractional derivative formula for the extended Wright function.

MSC:

33B15 Gamma, beta and polygamma functions
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
33C15 Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)
33E12 Mittag-Leffler functions and generalizations
33E50 Special functions in characteristic \(p\) (gamma functions, etc.)
44A15 Special integral transforms (Legendre, Hilbert, etc.)
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References:

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