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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 Carlson symmetric form ： ウィキペディア英語版 Carlson symmetric form In mathematics, the Carlson symmetric forms of elliptic integrals are a small canonical set of elliptic integrals to which all others may be reduced. They are a modern alternative to the Legendre forms. The Legendre forms may be expressed in terms of the Carlson forms and vice versa. The Carlson elliptic integrals are: :$R\_F(x,y,z)\; =\; \backslash tfrac\backslash int\_0^\backslash infty\; \backslash frac\backslash int\_0^\backslash infty\; \backslash frac\; \backslash int\_0^\backslash infty\; \backslash frac\; \backslash int\_0^\backslash infty\; \backslash frac$ and $\backslash scriptstyle$ are special cases of $\backslash scriptstyle$ and $\backslash scriptstyle$, all elliptic integrals can ultimately be evaluated in terms of just $\backslash scriptstyle$ and $\backslash scriptstyle$. The term ''symmetric'' refers to the fact that in contrast to the Legendre forms, these functions are unchanged by the exchange of certain of their arguments. The value of $\backslash scriptstyle$ is the same for any permutation of its arguments, and the value of $\backslash scriptstyle$ is the same for any permutation of its first three arguments. The Carlson elliptic integrals are named after Bille C. Carlson. ==Relation to the Legendre forms== 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「Carlson symmetric form」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.