Computational properties of three-term recurrence relations for Kummer functions

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...

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Veröffentlicht in:	Journal of computational and applied mathematics 2010-01, Vol.233 (6), p.1505-1510
Hauptverfasser:	Deaño, Alfredo, Segura, Javier, Temme, Nico M.
Format:	Artikel
Sprache:	eng
Schlagworte:	Asymptotic analysis Confluent hypergeometric functions Difference and functional equations, recurrence relations Exact sciences and technology Kummer functions Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical evaluation of special functions Sciences and techniques of general use Special functions Stability of recurrence relations
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Zusammenfassung:	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.
ISSN:	0377-0427 1879-1778
DOI:	10.1016/j.cam.2008.03.051