Second type Neumann series of generalized Nicholson function (Q2302205)

This paper deals with the use of special functions in infinite series of Neumann type. Closed form definite integral expressions are obtained for the second type Neumann series given by generalized Nicholson's functions, where these functions are represented by Bessel functions of the first and second kind. The closed form expressions are obtained with the aid of Dirichlet series' Cahen's integral form. The paper starts by giving applications and use of Hankel functions, Nicholson's functions (such as being a part of a generalized Jaeger integral), demonstrating its applications in many diverse fields of mathematics and other fields of science such as Integral equations, wave equation, heat flow, diffusion, electrochemistry, scattering problem of a plane wave, \ldots The paper also talks briefly about the history of Neumann series and its use and applications. The main goal of this paper is to obtain an integral representation formula for the second type Neumann series whose terms are the generalized Nicholson functions. The main result is given and proved by the statements and proofs of three theorems. The paper ends with Acknowledgements and References.