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Computation of Hyperspherical Bessel Functions

Part of: Difference and functional equations, recurrence relations

Published online by Cambridge University Press:  06 July 2017

Thomas Tram
Thomas Tram*
Affiliation:
Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark
*
*Corresponding author. Email address:thomas.tram@phys.au.dk (T. Tram)

Abstract

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In this paper we present a fast and accurate numerical algorithm for the computation of hyperspherical Bessel functions of large order and real arguments. For the hyperspherical Bessel functions of closed type, no stable algorithm existed so far due to the lack of a backwards recurrence. We solved this problem by establishing a relation to Gegenbauer polynomials. All our algorithms are written in C and are publicly available at Github [https://github.com/lesgourg/class_public]. A Python wrapper is available upon request.

Keywords

Hyperspherical Bessel functionsrecurrence relationsWKB approximationinterpolation

MSC classification

Secondary: 65Q30: Recurrence relations 65Z05: Applications to physics

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 3 , September 2017 , pp. 852 - 862
Copyright
Copyright © Global-Science Press 2017 

Footnotes

Communicated by Jie Shen

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