Fourth-order Bessel-type special functions: a survey

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review


  • W Everitt

Colleges, School and Institutes


This survey paper reports on the properties of the fourth-order Bessel-type linear ordinary differential equation, on the generated self-adjoint differential operators in two associated Hilbert function spaces, and on the generalisation of the classical Hankel integral transform. These results are based upon the properties of the classical Bessel and Laguerre second-order differential equations, and on the fourth-order Laguerre-type differential equation. From these differential equations and their solutions, limit processes yield the fourth-order Bessel-type functions and the associated differential equation.


Original languageEnglish
Title of host publicationDifference equations, special functions and orthogonal polynomials
Subtitle of host publicationProceedings of the International Conference Munich, Germany, 25 – 30 July 2005
EditorsS Elaydi, J Cushing, R Lasser, A Ruffing, V Papageorgiou , W Van Assche
Publication statusPublished - May 2007
EventProceedings of the International Conference - Germany, Munich, United Kingdom
Duration: 25 Jun 200530 Jun 2005


ConferenceProceedings of the International Conference
CountryUnited Kingdom