Arithmetic Means for a Class of Functions and the Modified Bessel Functions of the First Kind

Feng Qi, Shao-Wen Yao and Bai-Ni Guo
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Feng Qi: School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, Henan, China
Shao-Wen Yao: School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, Henan, China
Bai-Ni Guo: School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, Henan, China

Mathematics, 2019, vol. 7, issue 1, 1-14

Abstract: In the paper, by virtue of the residue theorem in the theory of complex functions, the authors establish several identities between arithmetic means for a class of functions and the modified Bessel functions of the first kind, present several identities between arithmetic means for a class of functions and infinite series, and find several series expressions for the modified Bessel functions of the first kind.

Keywords: arithmetic mean for function; modified Bessel function of the first kind; identity; series expression; residue theorem; Toader–Qi mean (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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