Computational properties of three-term recurrence relations for Kummer functions

Authors:
Alfredo Deaño;Javier Segura;Nico M. Temme
Affiliations:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, UK;Departamento de Matemáticas, Estadística y Computación, Univ. de Cantabria, 39005 Santander, Spain;CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 3
Cited 0

Coulomb and Bessel functions of complex arguments and order

Journal of Computational Physics
Uniform asymptotic expansions for Whittaker's confluent hypergeometric functions

SIAM Journal on Mathematical Analysis
Numerical Methods for Special Functions

Numerical Methods for Special Functions

Quantified Score

Hi-index	7.29

Visualization

Abstract

Several three-term recurrence relations for confluent hypergeometric functions are analyzed from a numerical point of view. Minimal and dominant solutions for complex values of the variable z are given, derived from asymptotic estimates of the Whittaker functions with large parameters. The Laguerre polynomials and the regular Coulomb wave functions are studied as particular cases, with numerical examples of their computation.