Abstract
Let Λ n denote the Lebesgue constant for Sinc approximation using n consecutive terms of the Sinc expansion of a function f. In this contribution we derive explicit values of a and b and the expression \(\varLambda_{n} = a\,\log (n) + b + \mathcal{O}(1/n^{2})\). We also provide graphic, illustrations of Lebesgue functions and Lebesgue constants for polynomial and Sinc approximations. These enable novel insights into the stability of these approximations in computation.
In honor of Paul Butzer’s 85th birthday
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The authors would like to thank the referee for his valuable remarks.
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Stenger, F., El-Sharkawy, H.A.M., Baumann, G. (2014). The Lebesgue Constant for Sinc Approximations. In: Zayed, A., Schmeisser, G. (eds) New Perspectives on Approximation and Sampling Theory. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-08801-3_13
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DOI: https://doi.org/10.1007/978-3-319-08801-3_13
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