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A class of polynomials related to those of Laguerre

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Polynômes Orthogonaux et Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1171))

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Abstract

We consider a class of polynomials, defined by l n (x)=(−1)n L n (x−n)(x), which are introduced by F.G. Tricomi. We explain the role of the polynomials in asymptotics, especially in uniform expansions of a Laplace-type integral. Moreover, an asymptotic expansion of l n(x) is given for n→∞ that refines results of Tricomi and Berg.

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References

  1. Berg, L., Uber eine spezielle Folge von Polynomen, Math. Nachr. 20, 152–158 (1959). See also: Uber gewisse Polynome von Tricomi, Math. Nachr. 24, 75 (1962).

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  2. Berg, L., Zur Abschätzung des Restgliedes in der asymptotischen Entwicklung des Exponential-integrals, Computing 18, 361–363 (1977).

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  5. Riekstins, E., The method of Stieltjes for error bounds of the remainder in asymptotic expansions (Russian), Akademiya Nauk Latviiskoi SSR, Institut Fiziki, Lafi-052 (1982).

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  6. Temme, N.M., Uniform asymptotic expansions of Laplace integrals, Analysis 3, 221–249 (1983).

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  7. Temme, N.M., Laplace type integrals: transformation to standard form and uniform asymptotic expansion, Report TW 240, Mathematisch Centrum, Amsterdam (1983); to appear in: Quart. Applied Mathem.

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  8. Tricomi, F.G.A class of non-orthogonal polynomials related to those of Laguerre, J. Analyse Math. 1, 209–231 (1951).

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Authors and Affiliations

  1. Centre for Mathematics and Computer Science, Kruislaan 413, 1098 SJ, Amsterdam, The Netherlands

    N. M. Temme

Authors
  1. N. M. Temme
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Editor information

Claude Brezinski André Draux Alphonse P. Magnus Pascal Maroni André Ronveaux

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© 1985 Springer-Verlag

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Temme, N.M. (1985). A class of polynomials related to those of Laguerre. In: Brezinski, C., Draux, A., Magnus, A.P., Maroni, P., Ronveaux, A. (eds) Polynômes Orthogonaux et Applications. Lecture Notes in Mathematics, vol 1171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076576

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  • DOI: https://doi.org/10.1007/BFb0076576

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16059-5

  • Online ISBN: 978-3-540-39743-4

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