| 翻訳と辞書 |
| Weierstrass M-test ： ウィキペディア英語版 |
Weierstrass M-test
In mathematics, the Weierstrass M-test is a test for showing that an infinite series of functions converges uniformly and absolutely. It applies to series whose terms are functions with real or complex values, and is analogous to the comparison test for determining the convergence of series of real or complex numbers.
== Statement ==
Weierstrass M-test. Suppose that is a sequence of real- or complex-valued functions defined on a set ''A'', and that there is a sequence of positive numbers satisfying
:
:
Then the series
:
converges uniformly on ''A''.
Remark. The result is often used in combination with the uniform limit theorem. Together they say that if, in addition to the above conditions, the set ''A'' is a topological space and the functions ''fn'' are continuous on ''A'', then the series converges to a continuous function.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「Weierstrass M-test」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|