Identifying minimal and dominant solutions for Kummer recursions
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- by Alfredo Deaño, Javier Segura and Nico M. Temme PDF
- Math. Comp. 77 (2008), 2277-2293 Request permission
Abstract:
We identify minimal and dominant solutions of three-term recurrence relations for the confluent hypergeometric functions $_1F_1(a+\epsilon _1 n;c+\epsilon _2 n;z)$ and $U(a+\epsilon _1 n,c+\epsilon _2 n,z)$, where $\epsilon _i=0,\pm 1$ (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 $|\arg z|<\pi$.References
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Additional Information
- Alfredo Deaño
- Affiliation: DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, CB3 0WA, United Kingdom
- Email: ad495@cam.ac.uk
- Javier Segura
- Affiliation: Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39005 Santander, Spain
- MR Author ID: 627158
- Email: javier.segura@unican.es
- Nico M. Temme
- Affiliation: CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
- Email: nicot@cwi.nl
- Received by editor(s): August 30, 2007
- Published electronically: May 14, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 77 (2008), 2277-2293
- MSC (2000): Primary 33C15, 39A11, 41A60, 65D20
- DOI: https://doi.org/10.1090/S0025-5718-08-02122-4
- MathSciNet review: 2429885