Note on the Dočev-Grosswald asymptotic series for generalized Bessel polynomials |
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Authors: | Herbert E Salzer |
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Institution: | 941 Washington Avenue, Brooklyn, NY 11225, USA |
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Abstract: | The Do?ev-Grosswald asymptotic series for the generalized Bessel polynomials yn(z; a, b) is extended to O(1/n4) relative accuracy. The differential equation of the asymptotic factor, derived from the differential equation for yn(z; a, b), is the basis of a different and easier method that employs simple recurrence relations and much less algebra for obtaining the same series. This is applied to the important special case of a = 1 to obtain the asymptotic series to O(1/n11) relative accuracy. |
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Keywords: | Primary 33A65 41A60 Generalized Bessel polynomials asymptotic series |
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