Convergence acceleration of Taylor sections by convolution
نویسنده
چکیده
Abstract. Taylor sections Sn(f) of an entire function f often provide easy computable polynomial approximants of f . However, while the rate of convergence of (Sn(f))n is nearly optimal on circles around the origin, this is no longer true for other plane sets as for example real compact intervals. The aim of this paper is to construct for certain families of (entire) functions sequences of polynomial approximants which are computable with essentially the same effort as Taylor sections and which have a better rate of convergence on some parts of the plane. The resulting method may be applied for example to (modified) Bessel functions, to confluent hypergeometric functions or to parabolic cylinder functions.
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