engleski

Integrals of ratios of Fox-Wright and incomplete Fox-Wright functions with applications

The main focus of the present paper is to establish definite integral formulae of ratios of the Fox-Wright functions. As consequences of the master formula, some novel integral formulae are derived for ratios of other special functions which are associated to Fox-Wright Psi function, like generalized hypergeometric function, modified Bessel function of the first kind and Mittag- Leffler type functions of two and three parameters. Moreover, closed integral form expressions are obtained for a family of Mathieu- type series and for the associated alternating versions whose terms contain the incomplete Fox- Wright function. As applications, functional bounding inequalities are established for the aforementioned series.

Complete and incomplete Fox-Wright function ; Generalized hypergeometric function ; Mittag-Leffler functions of two and three parameters ; Mathieu-type series ; Bilateral functional inequalities

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