Abstract
A heuristic method to construct uniform approximations to analytic transcendental functions is developed as a generalization of the Hermite-Padé interpolation to infinite intervals. The resulting uniform approximants are built from elementary functions using known series and asymptotic expansions of the given transcendental function. In one case (Lambert’s W function) we obtained a uniform approximation valid in the entire complex plane. Several examples of the application of this method to selected transcendental functions are given.
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© 2003 Springer-Verlag Berlin Heidelberg
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Winitzki, S. (2003). Uniform Approximations for Transcendental Functions. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44839-X_82
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DOI: https://doi.org/10.1007/3-540-44839-X_82
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