On the asymptotic expansions of entire functions defined by Maclaurin series
نویسندگان
چکیده
منابع مشابه
On Entire Functions Defined by a Dirichlet Series: Correction
1. As pointed out by Sunyer i Balaguer in the preceding paper the proofs of Theorem 1 and of the second part of Theorem 2 of our paper [l ] are faulty. We observe that if we impose the additional hypothesis that Afs(D), is a nonincreasing function for sufficiently small a then the proofs can be made to work. After correction Theorem 1 and the second part of Theore...
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The papers [15], [16], [4], [12], [2], [14], [5], [1], [3], [7], [6], [10], [11], [8], [9], [17], and [13] provide the notation and terminology for this paper. The following proposition is true (1) For every real number x and for every natural number n holds |x| = |x|. Let f be a partial function from R to R, let Z be a subset of R, and let a be a real number. The functor Maclaurin(f, Z, a) yie...
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There are several important observations to make about this definition. (i) The definition says that, for each fixed n, ∑n m=0 amx m becomes a better and better approximation to f(x) as x gets smaller. As x → 0, ∑m=0 amx approaches f(x) faster than x tends to zero. (ii) The definition says nothing about what happens as n → ∞. There is no guarantee that for each fixed x, ∑n m=0 amx m tends to f(...
متن کاملTaylor Series and Asymptotic Expansions
There are several important observations to make about this definition. (i) The definition says that, for each fixed n, ∑n m=0 amx m becomes a better and better approximation to f(x) as x gets smaller. As x → 0, ∑m=0 amx approaches f(x) faster than x tends to zero. (ii) The definition says nothing about what happens as n → ∞. There is no guarantee that for each fixed x, ∑n m=0 amx m tends to f(...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1944
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1944-08168-8