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Abstract: Let L k denote the Lebesgue constants of the Walsh system. The following exact result is established by means of Mellin transforms: Ln where F (u) is a continuous periodic function with period 1 whose Fourier coefficients can be explicitly expressed in terms of Riemann's zeta function. This improves an old result of Fine. (Update)
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BibTeX entry: (Update)
@misc{ hwang-asymptotic,
author = "Hsien-Kuei Hwang",
title = "Asymptotic Expansion for the Lebesgue Constants of the Walsh System",
url = "citeseer.ist.psu.edu/article/hwang95asymptotic.html" }
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61 Oxford University Press (context) - Titchmarsh, of - 1939
56 Asymptotic Approximations of Integrals (context) - Wong - 1989
28 Transactions of the American Mathematical Society (context) - Fine, Walsh - 1949
25 Mellin transforms and asymptotics: the mergesort recurrence - Flajolet, Golin - 1994
24 Mellin transforms and asymptotics: digital sums - Flajolet, Grabner et al. - 1994
11 the number of heaps and the cost of heap constructions - Hwang, Steyaert
9 The General Theory of Dirichlet's Series (context) - Hardy, Riesz - 1952
6 Walsh Series and Transforms---Theory and Applications (context) - Golubov, Efimov et al. - 1987
5 somme des chiffres (context) - Delange, fonction et al. - 1975
5 The constants of Landau and Lebesgue (context) - Watson - 1930
4 Asymptotic expansion of the Lebesgue constants associated wi.. (context) - Shivakumar, Wong - 1982
2 Asymptotic expansions of the Lebesgue constants for Jacobi s.. (context) - Frenzen, Wong - 1986
2 Asymptotic expansion of the Lebesgue constants associated wi.. (context) - Jiang - 1993
2 Operational Calculus Based on the Two-sided Laplace Integral (context) - van der Pol, Bremmer - 1987
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