Geometric convergence to e−z by rational functions with real poles
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In this paper, we show that there exists a sequence of rational functions of the formRn(z)=pn−1(z)/(1+z/n)n,n=1, 2, ..., with degpn−1≦n−1, which converges geometrically toe−z in the uniform norm on [0, +∞), as well as on some infinite sector symmetric about the positive real axis. We also discuss the usefulness of such rational functions in approximating the solutions of heat-conduction type problems.
KeywordsRational Function Mathematical Method Real Axis Type Problem Uniform Norm
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