Computation of the c -table related to the padé approximation

The aim of this paper is to give a complete and practical method for numerical application of padé approximation with the help of the c -table analysis. we present an exhaustive list of useful formulas to compute a c -table related to a formal power series c (z) =n = 0 ∞ c n z n. some of these formulas are not widely known,because they were presented in publications of limited circulation. some others were never published,as three symmetric paszkowski-like formulas to overcome the blocks in a c -table or an extension of local error formula for padé approximants in the blocks. all formulas are given in two versions: in terms of toeplitz determinants (c -table) and in the version of hankel determinants (c -table). we compare the theory with numerical observations by reproducing different computational aspects of software producing the c -tables with the presence of blocks and their evolution following the evolution of computer environment. © 2013 radosław jedynak and jacek gilewicz.