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A note on uniform approximation of functions having a double pole

Published online by Cambridge University Press:  01 May 2014

Ionela Moale
Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz (JKU), Altenbergerstr. 69, 4040 Linz, Austria email
Veronika Pillwein
Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz (JKU), Altenbergerstr. 69, 4040 Linz, Austria email


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We consider the classical problem of finding the best uniform approximation by polynomials of $1/(x-a)^2,$ where $a>1$ is given, on the interval $[-\! 1,1]$. First, using symbolic computation tools we derive the explicit expressions of the polynomials of best approximation of low degrees and then give a parametric solution of the problem in terms of elliptic functions. Symbolic computation is invoked then once more to derive a recurrence relation for the coefficients of the polynomials of best uniform approximation based on a Pell-type equation satisfied by the solutions.

Research Article
© The Author(s) 2014 


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