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ARTICLE

Determinantal Expressions and Recursive Relations for the Bessel Zeta Function and for a Sequence Originating from a Series Expansion of the Power of Modified Bessel Function of the First Kind

Yan Hong¹, Bai-Ni Guo^2,*, Feng Qi³
1 College of Mathematics and Physics, Inner Mongolia University for Nationalities, Tongliao, 028043, China
2 School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, 454003, China
3 School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China
* Corresponding Author: Bai-Ni Guo. Email:
Dedicated to Professor Dr. Mourad E. H. Ismail at University of Central Florida in USA
(This article belongs to this Special Issue: Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling)

Computer Modeling in Engineering & Sciences 2021, 129(1), 409-423. https://doi.org/10.32604/cmes.2021.016431

Received 05 March 2021; Accepted 07 June 2021; Issue published 24 August 2021

Abstract

In the paper, by virtue of a general formula for any derivative of the ratio of two differentiable functions, with the aid of a recursive property of the Hessenberg determinants, the authors establish determinantal expressions and recursive relations for the Bessel zeta function and for a sequence originating from a series expansion of the power of modified Bessel function of the first kind.

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Keywords

Determinantal representation; recursive relation; series expansion; first kind modified Bessel function; Bessel zeta function; Pochhammer symbol; gamma function; Hessenberg determinant

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Citations