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Zbl 1179.65027
Deaño, Alfredo; Segura, Javier; Temme, Nico M.
Computational properties of three-term recurrence relations for Kummer functions. (English)
[J] J. Comput. Appl. Math. 233, No. 6, 1505-1510 (2010). ISSN 0377-0427

Summary: 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.

MSC 2000:: *65D20 Computation of special functions
33F05 Numerical approximation of special functions
33C15 Confluent hypergeometric functions

Keywords: Kummer functions; confluent hypergeometric functions; stability of recurrence relations; asymptotic analysis; Whittaker functions; Laguerre polynomials; Coulomb wave functions; numerical examples

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