Neumann series

Árpád Baricz, Dragana Jankov Maširević, Tibor K. Pogány

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The goal of present chapter is to study in details the integral representations of the Neumann series (of the first and second type) of Bessel and modified Bessel functions of the first and second kind. In order to achieve our goal we use several methods: the Euler–Maclaurin summation technique, differential equation technique, fractional integration technique. Moreover, we present some interesting results on the coefficients of Neumann series, product of modified Bessel functions of the first and second kind and the cumulative distribution function of the non-central χ2-distribution.

Original languageEnglish
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Pages27-86
Number of pages60
DOIs
Publication statusPublished - Jan 1 2017

Publication series

NameLecture Notes in Mathematics
Volume2207
ISSN (Print)0075-8434

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'Neumann series'. Together they form a unique fingerprint.

  • Cite this

    Baricz, Á., Jankov Maširević, D., & Pogány, T. K. (2017). Neumann series. In Lecture Notes in Mathematics (pp. 27-86). (Lecture Notes in Mathematics; Vol. 2207). Springer Verlag. https://doi.org/10.1007/978-3-319-74350-9_2