Uniform Approximations for Transcendental Functions

  title={Uniform Approximations for Transcendental Functions},
  author={Sergei Winitzki},
A heuristic method to construct uniform approximations to analytic transcendental functions is developed as a generalization of the Hermite-Pade 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… 

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