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0
votes
1answer
59 views

How to substitute by NDSolve solution to plot a new function

Assume I got some function by NDSolve , like y(t) ...
4
votes
1answer
88 views

Real and imaginary parts of complex logarithm

I need to obtain the real and imaginary parts of the below expression with Mathematica: $(- i a - m^2) \ln(\frac{i m^2}{2 a})$, where $a$ and $m$ are real. So we have: ...
0
votes
0answers
34 views

Plotting NDSolve function in complex coordinates

I have this system of equations: $- \ddot{z} + \frac{1}{g} \frac{\partial g}{\partial z} \dot{z}^2 + \frac{1}{g} \frac{\partial g}{\partial z^*} \dot{z} \dot{z}^*$ =0 , $- \ddot{z}^*+ \frac{1}{g^*} ...
1
vote
3answers
75 views

Riemann surface of incomplete gamma function

Michael Trott in his book The Mathematica GuideBook for Symbolics, page 1003, has illustrated a nice way to visualize the Riemann surface of the incomplete gamma function $\Gamma[\alpha, z]$. To plot ...
1
vote
1answer
79 views

Plotting a function in 3 dimensions within a domain

In this paper: https://www.staff.science.uu.nl/~beuke106/HypergeometricFunctions/COGP.pdf Any help how to reproduce the plot in Figure:7 It’s the leading order of the complex function, Equation (...
1
vote
0answers
32 views

How to compute Bott-Chern operator ddc

I wish I could make Mathematica compute the $dd^c=2i\partial\bar\partial$ of a function depending on several complex variables. The question involves complex or Wirtinger derivatives (https://...
1
vote
1answer
54 views

visualizing branch cut of a complex function

I'm working in the plotting the branch cut of a complex function, namely: $w(z) = (2+z) \ln(2+z) - 2(1+z) \ln(1+z) + z \ln z$. To do so, I have tried this: ...
5
votes
1answer
127 views

Visualizing Riemann surface (two branches) of logarithm

I'm trying to plot two branches of the complex multi-valued function: (In a previous post - linked above-, Mathematica found the branch cut of the following function between -1 and 0) $1-z\ln[(1+z)/z]...
4
votes
2answers
167 views

To plot branch cut of logarithm

I like to see the branch cut of the function: $$1 - z \ln[(1+z)/z].$$ If I plot it in the complex plane: ...
0
votes
0answers
56 views

Unexpected difference between integral and summation?

I am trying to integrating something like: Integrate[Exp[-i*(k*x+k*z)]*Exp[-(x^2+z^2)],{x,-largenumber,largenumber},{z,-largenumber,largenumber}] My issue is that ...
0
votes
1answer
36 views

Interesting output in Integrate [closed]

I found interesting behaviour, best illustrated in the following example. When trying to evaluate Integrate[1/(d^2 - 1), d] Mathematica 11.3 gives the following ...
2
votes
2answers
632 views

Weird result in complex limit

I am trying to evaluate a limit: gamma[w_] = Sqrt[-(u*e)w^2 + I*(u*s)w]; Limit[Re[gamma[x]], {x -> DirectedInfinity[1]}] I calculated the limit by hand, and ...
10
votes
2answers
823 views

Why does Arg'[1. + I] return -0.5?

From the document we know that Arg[z] gives the gives the argument of the complex number z. Then how about ...
1
vote
3answers
85 views

How to take a derivative of a function with a real part taken

Consider f[x_]=Re[x^3] I now take the derivative of this D[f[x],x] and the result is ...
9
votes
3answers
722 views

How to use Mathematica to do a complex integrate with poles in real axis?

I want to use Mathematica to compute the following complex integral: Integrate[Exp[I z ] 1/z, {z, -Infinity, Infinity}] Mathematica reports that it does not ...
6
votes
2answers
196 views

Does Mathematica gives us a wrong result for the integral of a function including elliptic functions?

Calculus tells us that the differentiation of the integral of a function should be itself, but at least in one case Mathematica answers NO. I feel very confused. The new figure seems to bifurcate at ...
4
votes
3answers
169 views

Conjugate & Derivative

I have some problem with the derivative of the 'conjugate' expression: Here I define the functions: ...
0
votes
3answers
71 views

Solution… 2nd Transcendental Equation with Graphical method [closed]

If $ 2x^3 + \ln x = 5 $, then what is $ x $? For beginning we started to find a solution for equation $$ \begin{align}\label{eq:eq} \ln x + cx = b \tag{1} \end{align} $$ We know from W function ...
3
votes
1answer
178 views

What does “ Im' ” mean? [closed]

I am trying to take the curl/derivative of the function A. What does " Im' " mean here? Why does Mathematica attempt to take the derivative of the Im function here? ...
1
vote
1answer
112 views

Can this integral be calculated using Mathematica?

I have the following integral: $$ \int_{-\infty}^{\infty} \frac{\mathrm d\tau}{2\pi \mathrm i} \int_{-\infty}^{\infty} \frac{\mathrm d\tau'}{2\pi \mathrm i} \frac{\mathrm e^{-c^2(\tau - \tau')^2}}{(\...
0
votes
2answers
79 views

Problem in dealing with Sign function

Let my function be $f(x)=e^{|x|}$. I wish to find $f''(x)$, this can be done as- $f'(x)=$sgn$(x)e^{|x|}$ $f''(x)=$sgn$(x)^2e^{|x|} =e^{|x|}$ In Mathematica, I am trying to plot $f''(x)$, it ...
1
vote
2answers
88 views

Working with complex valued functions

I have a function which has real and imaginary parts and I need to differentiate both parts separately. This is a simpler example of what I have tried, without success: ...
0
votes
1answer
79 views

Using “if” to compare 2 expressions (Complex and real numbers)

Hello. I want to solve this cubic equation and compare the answers then I can assing the lower result to "VmL" and the greatest result to "VmG" but I have problems when the result is a complex number ...
2
votes
1answer
49 views

How to declare derivatives of a multivariable function as real in order to get Re and Im part of the expression?

Re and Im work properly, with appropriate assumptions, in the example like this ...
0
votes
0answers
36 views

Residues of products

i have the following problem: My function is given by: $(cz^{-1}+aq^{-j}-bq^{-2j}z)\prod_{m=1}^{Q-1}\frac{qz-z_{m}}{z-z_m}+(-cz^{-1}+dq^{j}+bq^{2j}z)\prod_{m=1}^{Q-1}\frac{q^{-1}z-z_{m}}{z-z_m}=E$, ...
15
votes
6answers
800 views

Is there a workaround for this integral?

The command Integrate[Exp[a*Exp[I*x]], {x, -Pi, Pi}] produces ConditionalExpression[0, a == 0] which is not correct in view of ...
1
vote
1answer
76 views

General result from Integrate differs from result with special values

Can someone explain why these outputs differ? ...
2
votes
0answers
82 views

Real integral giving complex result [duplicate]

I'm trying to calculate the following indefinite integral: $$ \int \log \left(\left(\frac{\lambda ^2}{a \lambda ^2+b}+\text{$\Delta $0}\right)^2\right) \, d\lambda $$ which is producing the ...
2
votes
2answers
88 views

Incorrect result for the region of convergence of a simple integral

Bug persisting at least through version 11.3.0 The standard Gaussian integral Integrate[Exp[-a x^2], {x,-Infinity,Infinity}] returns ...
2
votes
2answers
45 views

Multivariable differentiating by a complex conjugate

I recently ran into something that should be straight forward, but seems to be incredibly complex. If I define some function, f[x_,y_]:=x+y I wish to take the ...
2
votes
3answers
287 views

How to take derivative of the argument of an interpolating function

I am trying to plot the derivative of the argument of an interpolating function u[t, x] with respect to $x$. Here, u[t, x] is ...
1
vote
1answer
261 views

Contour integration with Mathematica

I seem to have difficulty getting Mathematica to evaluate contour integrals correctly. I am just parametrising them and inputting them in as usual but I am having problems. For example, consider $I=\...
9
votes
1answer
238 views

Contour integration, residues and precision of the poles

Task I am trying to evaluate the contour integral of some functions. To have a concrete example, let's use $$ f(z,s) = \frac{1+(4+2s)\, z}{z - \left( 9 + 35s + 24s^2 + 4s^3 \right) z^2 + 8z^3} $$ <...
4
votes
1answer
289 views

Wrong complex integral

I've tried to perform the following integral with mathematica (student edition): ...
2
votes
2answers
289 views

Tutorials on complex analysis

Where can I find some good tutorials (notebook files) about complex analysis theory & applications using Mathematica? Currently I can only find a book by Shaw.
3
votes
2answers
195 views

Why can’t mathematica find this residue?

I am trying to find the residue of the function $$f(z)=(z+1)^2e^{3/z^2}$$ at $z=0$. I tried the following in Mathematica Residue[(z+1)^2*Exp[3/z^2],{z,0}] which ...
1
vote
1answer
91 views

Evaluating Residue at pole with different forms

I want to evaluate residues at the poles of the function $\frac{1}{z^{3/2}+r^{3/2}}$ fun = 1/ (z^(3/2) + r^(3/2)); where z ...
7
votes
2answers
242 views

Possible bug with contour integration

I wanted to confirm the value of the integral $$\frac12\int_{\partial\Bbb D}\frac{\sin z}{\cosh z-1}\, dz$$ where $\partial\Bbb D$ is the boundary of the disk of radius $1$. Thus I had written the ...
2
votes
2answers
49 views

behavior of functions with parameters inside arguments

I don't understand this behavior: why does Limit[z/(z - a), z -> 0] give zero and not a condition depending on a, provided it ...
0
votes
1answer
201 views

Problem in computing residue

I need to integrate the following function $F(y)$ of complex variable $y$ over the unit circle $|y|=1$: ...
0
votes
1answer
63 views

Derivatives with respect to the independent variables $z\in\mathbb C$ and $\bar z$ [duplicate]

I want to be able to treat $z$ and its complex conjugate as independent variables, so that for instance $\partial (z\bar\,z)/\partial z = \bar z$. When I try to do this by evaluating ...
2
votes
0answers
128 views

Integral on unit disk of a function with two singularities

The goal is to prove, using Mathematica, that for $\mathbb{D}$ the unit disk and $u,v \in \mathbb{D}$, $u \neq v$, $$\frac{1}{\pi} \int_{\mathbb{D}} \frac{\mathrm{d}^2z}{(z-u)\overline{(z-v)}} = \ln(1-...
1
vote
2answers
268 views

Having problems integrating a function of a complex variable [closed]

I've tried to calculate the integral And I got the result $16i \pi ^3$. I wanted to check my calculation, so I ran this code in Mathematica: ...
2
votes
0answers
36 views

Linearity of the Conjugate operator

The output of Grad[Conjugate[x + y + z], {x, y, z}] is ...
0
votes
0answers
90 views

How to maximize the modulus of a multivariate complex-valued function?

My problem is the following. I have a messy, complex-valued function ...
4
votes
1answer
183 views

How to force a real function to appear with real components [closed]

The command Integrate oftentimes produces output that seems to be a mix of real and complex components even though the result is a real function. The question is ...
0
votes
2answers
91 views

Calculus of residues

I try to calculate the following residue ...
1
vote
0answers
262 views

Contour integral calculation [closed]

There is an integral of a complex function to calculate: $$ \oint_{|z|=2015}\frac{3i(z^3+z-2)}{\pi(z-3)}e^{-\frac{1}{z}}dz,$$ where the contour is a circle of radius 2015. Calculating it manually I ...
1
vote
2answers
79 views

Calculus Residue 3

I try to calculate f[z_]:=1/(Cosh[Sqrt[3]\[Pi] z ]-Cos[z \[Pi] ]) Assuming[k\[Element] Integers,Residue[f[z],{z,(2 I k)/(I+Sqrt[3])}]] but the answer is 0 maybe ...
0
votes
1answer
59 views

Calculus of residue

i try to do the following Assuming[k\[Element] Integers,Residue[Cos[x]/x^(k+1),{x,0}]] but any respond how to calculate for any k the k derivate of Cos function ...