Introduction and Preliminary Results

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We begin with a brief outline of Bessel functions, which will be needed in the next chapters. We recall here the Bessel, modified Bessel, spherical Bessel and modified spherical Bessel functions and define the generalized Bessel function. Some general properties of generalized Bessel functions are discussed in this chapter. These include: recursive formulas, differentiation formula, integral representations. We recall here also the Gaussian hypergeometric function with its basic properties which will have applications in Chap. 3. Finally, at the end of this chapter we list some classical inequalities which will be used in the sequel.

Original languageEnglish
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Pages1-22
Number of pages22
DOIs
Publication statusPublished - Jan 1 2010

Publication series

NameLecture Notes in Mathematics
Volume1994
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692

Fingerprint

Gaussian Hypergeometric Function
Spherical Functions
Hypergeometric Functions
Bessel Functions
Friedrich Wilhelm Bessel
Generalized Functions
Recursive Formula
Integral Representation

Keywords

  • Bessel Function
  • Gaussian Hypergeometric Function
  • Generalize Hypergeometric Function
  • Hypergeometric Function
  • Spherical Bessel Function

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Baricz, A. (2010). Introduction and Preliminary Results. In Lecture Notes in Mathematics (pp. 1-22). (Lecture Notes in Mathematics; Vol. 1994). Springer Verlag. https://doi.org/10.1007/978-3-642-12230-9_1

Introduction and Preliminary Results. / Baricz, A.

Lecture Notes in Mathematics. Springer Verlag, 2010. p. 1-22 (Lecture Notes in Mathematics; Vol. 1994).

Research output: Chapter in Book/Report/Conference proceedingChapter

Baricz, A 2010, Introduction and Preliminary Results. in Lecture Notes in Mathematics. Lecture Notes in Mathematics, vol. 1994, Springer Verlag, pp. 1-22. https://doi.org/10.1007/978-3-642-12230-9_1
Baricz A. Introduction and Preliminary Results. In Lecture Notes in Mathematics. Springer Verlag. 2010. p. 1-22. (Lecture Notes in Mathematics). https://doi.org/10.1007/978-3-642-12230-9_1
Baricz, A. / Introduction and Preliminary Results. Lecture Notes in Mathematics. Springer Verlag, 2010. pp. 1-22 (Lecture Notes in Mathematics).
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