Pade approximants of the Mittag-Leffler functions

被引：21
|
作者：
Starovoitov, A. P. [1 ]
Starovoitova, N. A. [1 ]
机构：
[1] Gomel State Univ, Gomel, BELARUS
来源：
SBORNIK MATHEMATICS | 2007年 / 198卷 / 7-8期
关键词：
D O I：
10.1070/SM2007v198n07ABEH003871
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is shown that for m <= n the Pade approximants {pi(n,m)(center dot;F-gamma)}, which locally deliver the best rational approximations to the Mittag-Leffler functions F-gamma, approximate the F-gamma as n -> infinity uniformly on the compact set D = {z : |z| <= 1} at a rate asymptotically equal to the best possible one. In particular, analogues of the well-known results of Braess and Trefethen relating to the approximation of exp z are proved for the Mittag-Leffler functions.
引用
收藏
页码：1011 / 1023
页数：13
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