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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 Lemniscatic elliptic function ： ウィキペディア英語版 Lemniscatic elliptic function In mathematics, a lemniscatic elliptic function is an elliptic function related to the arc length of a lemniscate of Bernoulli studied by Giulio Carlo de' Toschi di Fagnano in 1718. It has a square period lattice and is closely related to the Weierstrass elliptic function when the Weierstrass invariants satisfy ''g''2 = 1 and ''g''3 = 0. In the lemniscatic case, the minimal half period ω1 is real and equal to :$\backslash frac)\},\backslash qquad$ e_2=0,\qquad e_3=-\tfrac. The case ''g''2 = ''a'', ''g''3 = 0 may be handled by a scaling transformation. However, this may involve complex numbers. If it is desired to remain within real numbers, there are two cases to consider: ''a'' > 0 and ''a'' < 0. The period paralleogram is either a "square" or a "diamond". ==Lemniscate sine and cosine functions== The lemniscate sine and cosine functions ''sl'' and ''cl'' are analogues of the usual sine and cosine functions, with a circle replaced by a lemniscate. They are defined by :$\backslash operatorname(r)=s$ where :$r=\backslash int\_0^s\backslash frac(r)=c$ :$r=\backslash int\_c^1\backslash frac\backslash int\_0^1\backslash frac\{\backslash sqrt\{1-t^4\}\}=\; 0.8346\backslash ldots.$ 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「Lemniscatic elliptic function」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.