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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 Fresnel integrals ： ウィキペディア英語版 Fresnel integral Fresnel integrals, ''S''(''x'') and ''C''(''x''), are two transcendental functions named after Augustin-Jean Fresnel that are used in optics, which are closely related to the error function (erf). They arise in the description of far field Fresnel diffraction phenomena, and are defined through the following integral representations: $S(x)=\backslash int\_0^x\; \backslash sin(t^2)\backslash ,\backslash mathrmt,\backslash quad\; C(x)=\backslash int\_0^x\; \backslash cos(t^2)\backslash ,\backslash mathrmt.$ The simultaneous parametric plot of ''S''(''x'') and ''C''(''x'') is the Euler spiral (also known as the Cornu spiral or clothoid). Recently, they have been used in the design of highways and other engineering projects. == Definition == The Fresnel integrals admit the following power series expansions that converge for all ''x'': :$S(x)=\backslash int\_0^x\; \backslash sin(t^2)\backslash ,\backslash mathrmt=\backslash sum\_^(-1)^n\backslash frac$ :$C(x)=\backslash int\_0^x\; \backslash cos(t^2)\backslash ,\backslash mathrmt=\backslash sum\_^(-1)^n\backslash frac$ Some authors, including Abramowitz and Stegun, (eqs 7.3.1 – 7.3.2) use $\backslash fract^2$ for the argument of the integrals defining ''S''(''x'') and ''C''(''x''). To get these functions, multiply the above integrals by $\backslash sqrt\}$ and multiply the argument ''x'' by $\backslash sqrt\}$. 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「Fresnel integral」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.