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, AlfredoSegura, JavierTemme, 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 functionsWhittaker functionsConfluent hypergeometric functionsRecurrence relationsDifference equationsStability of recurrence relationsNumerical evaluation of special functionsAsymptotic analysis Rights: © AMS Appears in Collections: DM - GAMA - Artículos de Revistas