query: Modified Cauchy Integral Formula
positive_passages.docid: 11062
positive_passages.text: $f(z)=\frac1{2\pi i}\int_{\Gamma}\frac{f(\zeta)}{z-\zeta}d\zeta$ if $\lim_{z\to\infty}f(z)=0$ and $f$ is analytic in $|z|\ge1$
negative_passages.docid: 42525
negative_passages.text: Rearrangement and Cauchy
negative_passages.docid: 99186
negative_passages.text: Gaussian integral evaluation
negative_passages.docid: 15947
negative_passages.text: Validity of Substitutions in Integrals
negative_passages.docid: 91196
negative_passages.text: Complex Integration of $\int_0^\infty e^{-ax}\cos(bx)\,dx$
negative_passages.docid: 73131
negative_passages.text: Derivation of the gaussian integral
negative_passages.docid: 56867
negative_passages.text: Convergence proof that involves integral
negative_passages.docid: 24592
negative_passages.text: Computing complex integral with absolute value
negative_passages.docid: 108560
negative_passages.text: Proof of a Gaussian Integral property
negative_passages.docid: 9926
negative_passages.text: About the relation between $\int_{0}^{\infty}\frac{\cosh((\alpha-\beta)x)}{(\cosh(x))^{\alpha+\beta }} \,dx$ and $B(\alpha,\beta)$
negative_passages.docid: 152339
negative_passages.text: Complex-valued Fourier integral: $ \int_{ - \infty }^{ + \infty } {\frac{{\cos (ax)}}{{{x^2} + 1}}{e^{ - ibx}}\,\mathrm dx} $
negative_passages.docid: 133212
negative_passages.text: $\int_C \frac{\log z}{z-z_0} dz$ - Cauchy theorem with $z_0$ outside the interior of $\gamma$
negative_passages.docid: 107987
negative_passages.text: How do I calculate $u(w)=\int_0^\infty \frac{1-\cos(wt)}{t}\,e^{-t}\,dt$?
negative_passages.docid: 99113
negative_passages.text: Reverse Cauchy Schwarz for integrals
negative_passages.docid: 109857
negative_passages.text: Contour integral of analytic function with singularity
negative_passages.docid: 63988
negative_passages.text: General formula for evaluating integrals of the form $\displaystyle\int_0^\infty x^ae^{-bx}dx$
negative_passages.docid: 44058
negative_passages.text: Calculating half derivative of $x$ using Cauchy's repeated integral formula