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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Bernoulli polynomials ： ウィキペディア英語版 Bernoulli polynomials In mathematics, the Bernoulli polynomials occur in the study of many special functions and in particular the Riemann zeta function and the Hurwitz zeta function. This is in large part because they are an Appell sequence, i.e. a Sheffer sequence for the ordinary derivative operator. Unlike orthogonal polynomials, the Bernoulli polynomials are remarkable in that the number of crossings of the ''x''-axis in the unit interval does not go up as the degree of the polynomials goes up. In the limit of large degree, the Bernoulli polynomials, appropriately scaled, approach the sine and cosine functions. This article also discusses the Bernoulli polynomials and the related Euler polynomials, and the Bernoulli and Euler numbers. ==Representations== The Bernoulli polynomials ''B''''n'' admit a variety of different representations. Which among them should be taken to be the definition may depend on one's purposes. 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「Bernoulli polynomials」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.