Publication:
Identifying minimal and dominant solutions for Kummer recursions

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ISSN: 0025-5718 (Print)
ISSN: 1088-6842 (Online)
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2008-10
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American Mathematical Society
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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.
Description
17 pages, no figures.-- MSC2000 codes: Primary 33C15, 39A11, 41A60, 65D20.
MR#: MR2429885 (2009f:33004)
Keywords
Kummer functions, Whittaker functions, Confluent hypergeometric functions, Recurrence relations, Difference equations, Stability of recurrence relations, Numerical evaluation of special functions, Asymptotic analysis
Bibliographic citation
Mathematics of Computation, 2008, vol. 77, p. 2277-2293