engleski

(p, q)-extended Bessel and modified Bessel functions of the first kind

Inspired by certain recent extensions of the Euler's beta, Gauss hypergeometric and confluent hypergeometric functions [1], we introduce (p, q)- extended Bessel function J_{; ; ; \nu, p, q}; ; ; , the (p, q)- extended modified Bessel function I_{; ; ; ; \nu, p, q}; ; ; ; of the first kind of order \nu by making use two additional parameters in the integrand, as well as the (p, q)-extended Struve H_{; ; ; \nu, p, q}; ; ; and the modified Struve L_{; ; ; \nu, p, q}; ; ; functions. Systematic investigation of its properties, among others integral representations, bounding inequalites Mellin transforms (for all newly defined Bessel and Struve functions), complete monotonicity, Tur\'an type inequality, associated non- homogeneous differential-difference equations (exclusively for extended Bessel functions) are presented. Brief presentation of another members of Bessel functions family: spherical ultrashperical, Delerue hyper-Bessel and their modified counterparts and the Wright generalized Bessel function with links to their (p, q) - extensions are proposed.

(p ; q)-extended Beta function ; (p ; q)-extended Bessel and modified Bessel functions of first kind ; (p ; q)-extended Struve and modified Struve functions ; Integral representation ; Complete monotonicity ; Differential-difference equation ; Turan type inequality

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