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Identifying minimal and dominant solutions for Kummer recursions |
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| Authors: | Alfredo Deañ o Javier Segura Nico M. Temme. |
| Affiliation: | DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, CB3 0WA, United Kingdom ; Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39005 Santander, Spain ; CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands |
| Abstract: | We identify minimal and dominant solutions of three-term recurrence relations for the confluent hypergeometric functions  and  , where  (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  ,  and  , with  . |
| Keywords: | Kummer functions Whittaker functions confluent hypergeometric functions recurrence relations difference equations stability of recurrence relations numerical evaluation of special functions asymptotic analysis |
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