Skip to main content
×
×
Home

Computation of Hyperspherical Bessel Functions

  • Thomas Tram (a1)
Abstract

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.

Copyright
Corresponding author
*Corresponding author. Email address: thomas.tram@phys.au.dk (T. Tram)
Footnotes
Hide All

Communicated by Jie Shen

Footnotes
References
Hide All
[1] Polyanin, A. D. and Zaitsev, V. F., Handbook of exact solutions for ordinary differential equations. CRC Press, Boca Raton, 1995.
[2] Harrison, E. R., Normal modes of vibrations of the universe, Rev. Mod. Phys. 39 (Oct, 1967) 862882.
[3] Abbott, L. and Schaefer, R. K., A General, Gauge Invariant Analysis of the Cosmic Microwave Anisotropy, Astrophys. J. 308 (1986) 546.
[4] Kosowsky, A., Efficient computation of hyperspherical bessel functions, astro-ph/9805173.
[5] Johansson, F. et al., mpmath: a Python library for arbitrary-precision floating-point arithmetic (version 0.18), December, 2013.
[6] Gautschi, W., Computational aspects of three-term recurrence relations, SIAM Review 9 (Jan., 1967) 2482.
[7] Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P., Numerical recipes in C (2nd ed.): the art of scientific computing. Cambridge University Press, New York, NY, USA, 1992.
[8] Lentz, W. J., Generating bessel functions in mie scattering calculations using continued fractions, Appl. Opt. 15 (Mar, 1976) 668671.
[9] Thompson, I. and Barnett, A., Coulomb and bessel functions of complex arguments and order, Journal of Computational Physics 64 (1986) 490509.
[10] Langer, R. E., On the asymptotic solutions of ordinary differential equations, with reference to the stokes’ phenomenon about a singular point, Transactions of the American Mathematical Society 37 (1935) pp. 397416.
[11] Bender, C. and Orszag, S., Advanced mathematical methods for scientists and engineers. International series in pure and applied mathematics. McGraw-Hill, 1978.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
  • URL: /core/journals/communications-in-computational-physics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 25 *
Loading metrics...

Abstract views

Total abstract views: 131 *
Loading metrics...

* Views captured on Cambridge Core between 6th July 2017 - 18th September 2018. This data will be updated every 24 hours.