Uniform approximation by meromorphic functions having prescribed poles
نویسندگان
چکیده
منابع مشابه
UNIFORM APPROXIMATION OF sgn (x) BY RATIONAL FUNCTIONS WITH PRESCRIBED POLES
For a ∈ (0, 1) let Lm(a) be the error of the best approximation of the function sgn (x) on the two symmetric intervals [−1,−a]∪ [a, 1] by rational functions with the pole of degree 2k − 1 at the origin and of 2m − 1 at the infinity. Then the following limit exists lim m→∞ Lm(a) ( 1 + a 1− a )m− 1 2 (2m− 1) 1 2 = 2 π ( 1− a2 2a )k+ 1 2 Γ ( k + 1 2 ) .
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 1981
ISSN: 0025-5831,1432-1807
DOI: 10.1007/bf01450659