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Please use this identifier to cite or link to this item:
http://hdl.handle.net/10016/6634
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| Title: | Identifying minimal and dominant solutions for Kummer recursions |
| Author(s): | Deaño, Alfredo
Segura, Javier
Temme, Nico M. |
| Publisher: | American Mathematical Society |
| Issued date: | Oct-2008 |
| Citation: | Mathematics of Computation, 2008, vol. 77, p. 2277-2293 |
| URI: | http://hdl.handle.net/10016/6634 |
| ISSN: | 0025-5718 (Print)
1088-6842 (Online) |
| DOI: | 10.1090/S0025-5718-08-02122-4 |
| Description: | 17 pages, no figures.-- MSC2000 codes: Primary 33C15, 39A11, 41A60, 65D20.
MR#: MR2429885 (2009f:33004) |
| Abstract: | We identify minimal and dominant solutions of three-term recurrence relations for the confluent hypergeometric functions $$ {}_1F_1(a+\epsilon_1n;c+\epsilon_2n;z) {and} U(a+\epsilon_1n,c+\epsilon_2n,z), $$ where $\epsilon_i=0, \pm1$ (not both equal to 0). The results are obtained by applying Perron's theorem, together with uniform asymptotic estimates derived by T. M. Dunster for Whittaker functions with large parameter values. The approximations are valid for complex values of a, c and z, with rg z < π. |
| Sponsor: | The authors acknowledge financial support from Ministerio de Educación y Ciencia, project MTM2006–09050. |
| Review: | PeerReviewed |
| Publisher version: | http://dx.doi.org/10.1090/S0025-5718-08-02122-4 |
| Keywords: | Kummer functions
Whittaker functions
Confluent hypergeometric functions
Recurrence relations
Difference equations
Stability of recurrence relations
Numerical evaluation of special functions
Asymptotic analysis |
| Rights: | © AMS |
| Appears in Collections: | DM - GAMA - Artículos de Revistas
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