Fourth-order Bessel-type special functions: a survey

W Everitt

doi:10.1142/9789812770752_0016

Fourth-order Bessel-type special functions: a survey

W Everitt

Mathematics

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

Abstract

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 language	English
Title of host publication	Difference equations, special functions and orthogonal polynomials
Subtitle of host publication	Proceedings of the International Conference Munich, Germany, 25 – 30 July 2005
Editors	S Elaydi, J Cushing, R Lasser, A Ruffing, V Papageorgiou , W Van Assche
Publisher	World Scientific
Pages	189-212
Number of pages	24
ISBN (Electronic)	978-9814475464
ISBN (Print)	978-9812706430
DOIs	https://doi.org/10.1142/9789812770752_0016
Publication status	Published - May 2007
Event	Proceedings of the International Conference - Germany, Munich, United Kingdom Duration: 25 Jun 2005 → 30 Jun 2005

Conference

Conference	Proceedings of the International Conference
Country/Territory	United Kingdom
City	Munich
Period	25/06/05 → 30/06/05

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Everitt, W. (2007). Fourth-order Bessel-type special functions: a survey. In S. Elaydi, J. Cushing, R. Lasser, A. Ruffing, V. Papageorgiou , & W. Van Assche (Eds.), Difference equations, special functions and orthogonal polynomials: Proceedings of the International Conference Munich, Germany, 25 – 30 July 2005 (pp. 189-212). World Scientific. https://doi.org/10.1142/9789812770752_0016

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title = "Fourth-order Bessel-type special functions: a survey",

abstract = "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.",

author = "W Everitt",

year = "2007",

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doi = "10.1142/9789812770752_0016",

language = "English",

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booktitle = "Difference equations, special functions and orthogonal polynomials",

publisher = "World Scientific",

note = "Proceedings of the International Conference ; Conference date: 25-06-2005 Through 30-06-2005",

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Everitt, W 2007, Fourth-order Bessel-type special functions: a survey. in S Elaydi, J Cushing, R Lasser, A Ruffing, V Papageorgiou & W Van Assche (eds), Difference equations, special functions and orthogonal polynomials: Proceedings of the International Conference Munich, Germany, 25 – 30 July 2005. World Scientific, pp. 189-212, Proceedings of the International Conference, Munich, United Kingdom, 25/06/05. https://doi.org/10.1142/9789812770752_0016

Fourth-order Bessel-type special functions: a survey. / Everitt, W.
Difference equations, special functions and orthogonal polynomials: Proceedings of the International Conference Munich, Germany, 25 – 30 July 2005. ed. / S Elaydi; J Cushing; R Lasser; A Ruffing; V Papageorgiou ; W Van Assche. World Scientific, 2007. p. 189-212.

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

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N2 - 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.

AB - 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.

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A2 - Cushing, J

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A2 - Van Assche, W

PB - World Scientific

Y2 - 25 June 2005 through 30 June 2005

ER -

Fourth-order Bessel-type special functions: a survey

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