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Computational properties of three-term recurrence relations for Kummer functions |
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| Authors: | Alfredo Deañ o,Javier Segura |
| Affiliation: | a Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, UK b Departamento de Matemáticas, Estadística y Computación, Univ. de Cantabria, 39005 Santander, Spain c CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands |
| 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. |
| Keywords: | 33C15 39A11 41A60 65D20 |
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