Integration of complex variables using Laurent series about a contour, C
I’ve got a homework question that I believe requires me to use Laurent series/method of residues. The question itself is: Evaluate $ \int_C \frac{1}{z^2(z^2-16)}$ where C is the contour $ |z| = 1$ ....
View ArticleParallelise numerical integral for contour plot
I have the following integral that I would like to evaluate: A[x_, y_] := 2/\[Pi] ((-1)^x y^x)/(2 - y)^(1 + x); Pintegrand[m_, n_, r1_, r2_, \[Theta]1_, \[Theta]2_] := (A[m, \[Tau]] A[n,...
View Articlelet $I_{p,q}=\int_{\gamma}p(z)\overline{q(z)}dz$ where $\gamma$ is the closed...
Consider the polynomial $ p(z),q(z)$ in the complex variable $ z$ and let $ I_{p,q}=\int_{\gamma}p(z)\overline{q(z)}dz$ where $ \gamma$ is the closed contour $ \gamma(t)=e^{it},0\leq t \leq 2\pi.$...
View ArticleHow to add labels in a contour plot using ggplot2?
I’m doing a contour plot with ggplot2 and I’m trying to add the labels like this tutorial. However, always appears the following error: Error in geom_text_contour(aes(z = z)) : could not find function...
View ArticlePerron’s formula where the integrand of the contour is badly behaved at (and...
I am attempting to use Perron’s formula to recover the asymptotic form of a summatory function. Namely, it can be shown (is not difficult to prove) that for the prime omega function, $ \omega(n)$ ,...
View ArticleHow to super impose a curve onto a 2-D contour plot
I have created a smooth color gradient 2-D contour plot with existing compiled data. I have an x-axis, y-axis, and z-data contour plotted as a colormap. I have a single value of z-data that I want to...
View Articlecontour plot problem
I have tried everything I think but I could not obtain a 3d contour plot from a list. Here is my code. Could you help me what the mistake I make ? data = {{0., 0.0416667, 0.0103448, -22952.9}, {0.,...
View ArticleContour pushing algorithm
I’m implementing push contour feature for web application. It is an ability to change the contour by touching it. Mouse pointer becomes a circle that bumps contour (like in Photoshop). Contour is...
View ArticleRemove mesh triangles in contour plot
How do I get rid of the mesh in this contour plot? ContourPlot[x^2 + y^2, {x, -10, 10}, {y, -10, 10}, Contours -> {1.0, 4.0, 10.5}, ContourStyle -> None, ContourShading -> {RGBColor[1, .2, 0,...
View ArticleNumerical contour integral
I am trying to compute the double integral for fixed $ m,z>0$ : Integrate[(Gamma[y/2] Sqrt[Gamma[3 - y]/Gamma[y]])/ Gamma[(3 - y)/2] z^(3 - y) (Exp[-m x] - 1) x^(y - 3)/x, {x, 0, \[Infinity]},{y,...
View ArticleHow to contour plot a quantized function?
I am trying to plot a function over a 2 dimensional region, which takes integer and half integer values. However, due to numerical approximations and errors, the calculated value of the function...
View ArticleContour integral does not converge
I have this integral where I want to evaluate it on the imaginary axis. However, it says that it does not converge even though I have introduced a small indentation $ a$ , function[z_] := 1/(Sinh[z/2]...
View ArticlePlotting an oriented contour
I’d like to add at least one arrow to a closed contour in the plane to show that e.g. a circumference is counterclockwise oriented. If I use e.g. ParametricPlot[ReIm[Exp[I t]], {t, 0, 2 \[Pi]}] how...
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