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Zbl 0556.33010
Frenzen, C.L.; Wong, R.
Asymptotic expansions of the Lebesgue constants for Jacobi series. (English)
[J] Pac. J. Math. 122, 391-415 (1986). ISSN 0030-8730

Explicit expressions are obtained for the implied constants in the two O- terms in Lorch's asymptotic expansions of the Lebesgue constants associated with Jacobi series [L. Lorch, Am. J. Math. 81, 875-888 (1959; Zbl 0095.049)]. In particular, a question of Szegö concerning asymptotic monotonicity of the Lebesgue constants for Laplace series is answered. Our method differs from that of Lorch, and makes use of some recently obtained uniform asymptotic expansions for the Jacobi polynomials and their zeros.

MSC 2000:: *33C45 Orthogonal polynomials and functions of hypergeometric type
41A60 Asymptotic problems in approximation
42C10 Fourier series in special orthogonal functions

Keywords: Lorch's asymptotic expansions of the Lebesgue constants; Jacobi series; Lebesgue constants for Laplace series; uniform asymptotic expansions for the Jacobi polynomials; Lebesgue constants for Jacobi series

Citations: Zbl 0095.049; Zbl 0556.33011

Cited in: Zbl 0556.33011

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