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
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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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