Mathematics – Numerical Analysis
Scientific paper
2003-06-20
Mathematics
Numerical Analysis
11 pages, LaTeX2e, 0 figures. o Appear in the Proceedings (Numerical Algorithms) of the International Conference on Numerical
Scientific paper
10.1023/A:1025517617217
Power series representations for special functions are computationally satisfactory only in the vicinity of the expansion point. Thus, it is an obvious idea to use instead Pad\'{e} approximants or other rational functions constructed from sequence transformations. However, neither Pad\'{e} approximants nor sequence transformation utilize the information which is avaliable in the case of a special function -- all power series coefficients as well as the truncation errors are explicitly known -- in an optimal way. Thus, alternative rational approximants, which can profit from additional information of that kind, would be desirable. It is shown that in this way a rational approximant for the digamma function can be constructed which possesses a transformation error given by an explicitly known series expansion.
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