Uniform approximations for transcendental functions

  • Authors:
  • Serge Winitzki

  • Affiliations:
  • Department of Physics, Ludwig-Maximilians University, Munich, Germany

  • Venue:
  • ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
  • Year:
  • 2003

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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.