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cauchy_principal_value [2014/02/22 18:56] nikolaj |
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| === Examples === | === Examples === | ||
| - | $\mathcal P\int_{-3}^7\left(\lambda x.\frac{1}{x}\right)=\int_{-3}^{-\varepsilon}\frac{1}{x}\,\mathrm dx+\int_{\varepsilon}^{7}\frac{1}{x}\,\mathrm dx=\left(\log(-\varepsilon)-\log(-3)\right)+\left(\log(7)-\log(\varepsilon)\right)=\log(\frac{7}{3})$ | + | $\mathcal P\int_{-3}^7\left(\lambda x.\frac{1}{x}\right)=\int_{-3}^{-\varepsilon}\frac{1}{x}\,\mathrm dx+\int_{\varepsilon}^{7}\frac{1}{x}\,\mathrm dx=\left(\log\left|-\varepsilon\right|-\log\left|-3\right|\right)+\left(\log\left|7\right|-\log\left|\varepsilon\right|\right)=\log\left|\frac{7}{3}\right|$ |
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Cauchy_principal_value|Cauchy principal value]] | Wikipedia: [[http://en.wikipedia.org/wiki/Cauchy_principal_value|Cauchy principal value]] | ||
