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Computational properties of three-term recurrence relations for Kummer functions

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URI: https://hdl.handle.net/10016/6737
ISSN: 0377-0427
DOI: 10.1016/j.cam.2008.03.051
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computational_deano_jcam_2010_ps.pdf (114.87 KB)
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2010-01-15
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Elsevier
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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.
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6 pages, 3 figures.-- MSC2000 codes: 33C15; 39A11; 41A60; 65D20.-- Issue title: "Special Functions, Information Theory, and Mathematical Physics. Special issue dedicated to Professor Jesús Sánchez Dehesa on the occasion of his 60th birthday".
Zbl#: Zbl pre05650069
Keywords
Kummer functions, Confluent hypergeometric functions, Stability of recurrence relations, Numerical evaluation of special functions, Asymptotic analysis
Bibliographic citation
Journal of Computational and Applied Mathematics, 2010, vol. 233, n. 6, p. 1505-1510
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