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In this paper, we propose an extension of the classical Bessel function by means of our $\ell$-hypergeometric function \cite{mhc-bid2015}. As the main results, the infinite order differential equation, the generating function relation, and contour integral representations including Schl\"{a}fli's integral analogue are derived. With the aid of these, other results including some inequalities are also obtained. At the end, the graphs of these functions are plotted using the Maple software.
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참고문헌 (11)
참고문헌 신청
N. Barnaby / 2008 / Dynamics with infinitely many derivatives: the initial value problem / J. High Energy Phys 2008(2)
Meera H. Chudasama / 2016 / Some new class of special functions suggested by the confluent hypergeometric function / ANNALI DELL'UNIVERSITA' DI FERRARA 62(1):23~38
M. H. Chudasama / 2019 / A new class of functions suggested by the generalized hypergeometric function / An. S¸tiint¸. Univ. Al. I. Cuza Ia¸si. Mat 65(1):19~36
A. Erd´elyi / 1953 / Higher transcendental functions. Vols. I / McGraw-Hill Book Company, Inc
V. Kiryakova / 1994 / Generalized fractional calculus and applications / Longman Scientific & Technical
Meera H. Chudasama / 2016 / Some new class of special functions suggested by the confluent hypergeometric function / ANNALI DELL'UNIVERSITA' DI FERRARA 62(1):23~38
M. H. Chudasama / 2019 / A new class of functions suggested by the generalized hypergeometric function / An. S¸tiint¸. Univ. Al. I. Cuza Ia¸si. Mat 65(1):19~36
A. Erd´elyi / 1953 / Higher transcendental functions. Vols. I / McGraw-Hill Book Company, Inc
V. Kiryakova / 1994 / Generalized fractional calculus and applications / Longman Scientific & Technical
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