Sturm–Liouville Problem and I–Bessel Sampling

Abstract

Abstract:The main aim of this article is to establish summation formulae in form of the sampling expansion series building the kernel function by the samples of the modified Bessel function of the first kind I ν , and to obtain a sharp truncation error upper bound occurring in the derived sampling series approximation. Summation formulae for functions I ν+1 /I ν , 1/I ν , I 2 ν and the generalized hypergeometric function 2 F 3 are derived as a by-product of these results. The main derivation tools are the Sturm-Liouville boundary value problem and various properties of Bessel and modified Bessel functions.Keywords: Bessel function of the first kind J ν , modified Bessel function of the first kind I ν , sampling series expansions, Sturm-Liouville boundary value problems, generalized hypergeometric function 2 F 3 , Fox-Wright generalized hypergeometric function p Ψ * q , sampling series truncation error upper bound.