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

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