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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 Kelvin function ： ウィキペディア英語版 Kelvin functions In applied mathematics, the Kelvin functions ber''ν''(''x'') and bei''ν''(''x'') are the real and imaginary parts, respectively, of :$J\_\backslash nu\; \backslash left\; (x\; e^\}\; \backslash right\; ),\backslash ,$ where ''x'' is real, and , is the νth order Bessel function of the first kind. Similarly, the functions Kerν(''x'') and Keiν(''x'') are the real and imaginary parts, respectively, of :$K\_\backslash nu\; \backslash left\; (x\; e^\}\; \backslash right\; ),\backslash ,$ where is the νth order modified Bessel function of the second kind. These functions are named after William Thomson, 1st Baron Kelvin. While the Kelvin functions are defined as the real and imaginary parts of Bessel functions with ''x'' taken to be real, the functions can be analytically continued for complex arguments With the exception of Ber''n''(''x'') and Bei''n''(''x'') for integral ''n'', the Kelvin functions have a branch point at ''x'' = 0. Below, is the Gamma function and is the Digamma function. == ber(''x'') == For integers ''n'', ber''n''(''x'') has the series expansion :$\backslash mathrm\_n(x)\; =\; \backslash left(\backslash frac\backslash right)^n\; \backslash sum\_\; \backslash frac"\; TITLE="\backslash left(\backslash frac">+\; \backslash frac\backslash right)\backslash pi\backslash right\; )\}\; \backslash left(\backslash frac\backslash right)^k$ where is the Gamma function. The special case ber0(''x''), commonly denoted as just ber(''x''), has the series expansion :$\backslash mathrm(x)\; =\; 1\; +\; \backslash sum\_\; \backslash frac\; \backslash left(\backslash frac\; \backslash right\; )^$ and asymptotic series :$\backslash mathrm(x)\; \backslash sim\; \backslash frac\}\}\}(x)\}$, where :$\backslash alpha\; =\; \backslash frac,$ :$f\_1(x)\; =\; 1\; +\; \backslash sum\_\; \backslash frac\; \backslash prod\_^k\; (2l\; -\; 1)^2$ :$g\_1(x)\; =\; \backslash sum\_\; \backslash frac\; \backslash prod\_^k\; (2l\; -\; 1)^2$ 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「Kelvin functions」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.