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The bounds for the error term of an asymptotic approximation of Jacobi polynomials

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1329)

Abstract

We consider a new asymptotic approximation of Jacobi polynomials P (α,β)n (cosϑ) and we obtain a realistic and explicit bound for the corresponding error term. The approximation is of Hilb's type and is uniformly valid for 0<ϑ≤π−ε, ε>0. Bounds for the error term in the asymptotic approximation of the zeros of P (α,β)n (cosϑ) are also given.

Keywords

  • Error Term
  • Bessel Function
  • Asymptotic Approximation
  • Asymptotic Representation
  • Jacobi Polynomial

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work was supported by the Consiglio Nazionale delle Ricerche of Italy and by the Ministero della Pubblica Istruzione of Italy.

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© 1988 Springer-Verlag

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Baratella, P., Gatteschi, L. (1988). The bounds for the error term of an asymptotic approximation of Jacobi polynomials. In: Alfaro, M., Dehesa, J.S., Marcellan, F.J., Rubio de Francia, J.L., Vinuesa, J. (eds) Orthogonal Polynomials and their Applications. Lecture Notes in Mathematics, vol 1329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083360

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  • DOI: https://doi.org/10.1007/BFb0083360

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19489-7

  • Online ISBN: 978-3-540-39295-8

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