Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.
0
votes
1answer
48 views
Plot $ g(r) = \int_0^\pi J_0(w\ r)\ \mathrm dw $
I want to plot $g(r)$ as a function of $r$ but $g(r)$ at each value of $r$ is an integral of the Bessel function over the the limits of $w$.
2
votes
2answers
66 views
Plotting a function $\psi(\rho,\theta,\phi)$ in spherical coordinates
If I want to plot the function
$\qquad \psi(\rho,\theta,\phi)=\frac{1}{8}\left(\frac{1}{\pi}\right)^{1/2}\rho e^{-\rho/2}sin(\theta)e^{-i\phi}$,
for which I wrote the code
...
0
votes
2answers
49 views
Global minimum of a function in a specified interval
I've got the following definition of fun1.
epsilon = 10^(-8)
fun1[h_] := (2 epsilon*Abs[Cos[1]]/h ) + (h*Abs[Cos[1]]/2)
Let'...
0
votes
0answers
25 views
Do these expansions make sense?
I mean
Series[DiracDelta[x], {x, 0, 3}]
$$ \delta (0)+O\left(x^4\right)+\frac{1}{6} \delta ^{(3)}(0) x^3+\frac{1}{2} x^2 \delta ''(0)+x \delta '(0)$$
and
<...
0
votes
1answer
28 views
Model fitting for concave curve: test if asymptote or convergence exist
I am asking a double check if conceptually I set up proper model and proceeding in good direction to drive conclusions.
I have a distribution that looks like this:
I want to test if for increasing x ...
0
votes
0answers
50 views
Constructing a user function with an integral
Maybe this is a basic task to perform but I haven't found any literature. I am performing a convolution of two functions:
...
0
votes
2answers
50 views
Solving for upper bound of integral with known value
I'm trying to calculate the upper bound of an integral. My current code is
f[r_?NumericQ] =
(1/(Pi*a^3))*4*Pi*(r^2)*E^(-r/a);
Plot[f[r], {r, 0, 1}]
When I ...
1
vote
1answer
66 views
Tangent point in Polar Coordinates
I don't know which command to determine the tangent lines that are parallel to the line $x=0$ (i.e. the y-axis) in Polar Coordinates. Can you help me please to give me some suggestions?
I attach some ...
0
votes
0answers
40 views
Indefinite integration of products of Bessel functions [on hold]
Is there any way to solve any of the following indefinite integrals in Mathematica?
...
0
votes
0answers
18 views
To prove F is irrotational and to find its scalar potential [closed]
F=(y^2 cosx+z^3)i+(2y sinx-4)j+(3xz^2)k
Show that F is irrotational and find its scalar potential
1
vote
1answer
47 views
Strange behaviour in derivative of Floor function
The function Floor[x] is piecewise constant, hence its derivatives should be piecewise zero.
This is far from true in Mathematica
In[497]:= $Version
Out[497]= "10.1.0 for Microsoft Windows (64-...
0
votes
2answers
37 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 ...
2
votes
1answer
239 views
How do I label critical points on the plot of a curve?
I want to label the local maxima, local minima, and points of inflection on a plot of a curve. How is this done in Mathematica?
1
vote
2answers
59 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:
...
3
votes
1answer
48 views
General integral does not match special case?
Consider the following function:
f = (E^(2 I c \[Phi]) - (E^(2 I \[Phi]))^c) (E^(2 I \[Phi]))^n
Integrating this function with respect to ...
0
votes
1answer
39 views
Relations between Function Variables in Computations
I have the relation λ=c/f, respectively f=c/λ and a simple function n[λ_]:=λ²+1. I'd like to differentiate the function with respect to f, then plot it as a function of λ again. For this, I can define ...
3
votes
1answer
152 views
How can I get the exact answer of the maximum of this function?
I am trying to find the maximum of a fuction: $ f(x)=\sqrt{x^2+9}-\sqrt{x^2-\sqrt{3} x+1} $.
I tried
Maximize[Sqrt[x^2 + 9] - Sqrt[x^2 - Sqrt[3]*x + 1], x]
and ...
1
vote
0answers
38 views
Simplyfing a quotient of polynomials [on hold]
I am trying to simplify some quotient of polynomials. In this case, they are really easy but I will have to deal with way harder expression and I wanna know how to do it in full generality. An example ...
0
votes
1answer
59 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 ...
7
votes
1answer
173 views
Inconsistency in Mathematica of whether integral diverges or not?
Consider the following (beta function) integral
Integrate[(1 - x)^a x^b, {x, 0, 1}]
ConditionalExpression[(Gamma[1 + a] Gamma[1 + b])/Gamma[2 + a + b], Re[b]>-...
5
votes
1answer
72 views
Annulus distribution in n dimensions: normalising constant, normed mean and variance
I would like to know the normalising constant of a distribution which has the pdf,
$$f(x) \propto \sqrt{\frac{1}{2\pi\sigma^2}}\text{exp}(-\frac{(|x|-r_0)^2}{\sigma^2}),$$
where $x\in\mathbb{R}^d$ ...
0
votes
0answers
25 views
NIntegrate failed to perform the integration unless AdaptiveMonteCarlo method is chosen
I have multi-dimensional numerical integration of some function depending on one parameter. If no specification for the integration method is chosen, the output for specific values of the parameters ...
1
vote
1answer
113 views
DiracDelta convergence in 3D - Cartesian vs. spherical coordinates
Integrating DiracDelta in 3D in Cartesian coordinates works just fine i.e. gives vecf[{x, y, z}]
...
1
vote
1answer
59 views
Plot of integral of summed `Sinc` series is incorrect
I have curve given by summing a small, finite series of Sinc functions, and I want to plot both the curve and its integral. In principle, it's easy:
...
0
votes
0answers
32 views
Gaussian probability distribution for a delta correlated variable [migrated]
I read in a paper that I have a vector $\bf{x}$ such that
$$
\langle x_i (t) x_j (t')\rangle=\delta_{ij}\delta(t-t')
$$
and the probability distribution for $\bf{x(t)}$ is a ...
0
votes
2answers
73 views
Continuous summation of a function [closed]
I have a simple function:
func =x Sin[π x]^2
This creates a curve that oscillates between 0 and values that increase linearly ...
0
votes
0answers
12 views
Gaussian distribution for delta correlated random variables [migrated]
I read in a paper that
"I have a vector $\bf{x}$ such that $\langle x_i (t) x_j
> (t')\rangle=\delta_{ij}\delta(t-t')$ and the probability distribution
for $\bf{x(t)}$ is a Gaussian ...
2
votes
1answer
34 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
...
1
vote
1answer
44 views
Eliminating Gamma from result of integration
I think the following integration result can be shown without Gamma.
Can anyone explain
Why Mathematica Uses Gamma.
How to ...
2
votes
2answers
78 views
Integration with Bessel function as result
When I try to calculate this integral,
1/(2*Pi)*Integrate[ Exp[I*2*θ]*Cos[1/2 (7 + Cos[θ])], {θ, 0, 2*Pi}]
Mathematica is unable to compute it. But the result ...
4
votes
1answer
87 views
Limit ArcTanh: different results in v10.4 and v11.3
I find a different results when computing limits with ArcTanh in version 10 and 11 of Mathematica.
The problem emerges with the following function
...
0
votes
0answers
44 views
0
votes
1answer
88 views
How can I assign first evaluate an Integrate command and then assign the integrated expression to a function?
I am trying to evaluate this integral?
$$\int_0^1\int_0^1 \frac{\mathrm dt\mathrm ds}{(c^2 + 2se + as^2 - 2tf - 2tsd + bt^2)^2}$$
I tried to do using the definite integral, but these two didn't ...
0
votes
0answers
35 views
Residues of products
i have the following problem:
My function is given by:
$(cz^{-1}+aq^{-j}-bq^{-2j}z)\prod_{m=1}^{Q-1}\frac{qz-z_{m}}{z-z_m}+(-cz^{-1}+dq^{j}+bq^{2j}z)\prod_{m=1}^{Q-1}\frac{q^{-1}z-z_{m}}{z-z_m}=E$,
...
2
votes
1answer
86 views
How do I evaluate the limit of $(x-5+\sqrt{x+1})/\sqrt{x^2-9}$ as $x \to 3$? [closed]
I tried substitution first. It won't work for this one.
When finding a limit of a fraction and in doubt, rationalize either the numerator or denominator.
0
votes
0answers
33 views
Correcting integration error by supplying assumptions
I wrote some auxiliary functions to help evaluate my main function ELC, which always return the error
Unable to prove that integration limits {0, t} are real. ...
15
votes
6answers
780 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
...
3
votes
2answers
112 views
2
votes
1answer
100 views
How to compute many sums or tables efficiently
I have some questions about programming in Mathematica and I would really appreciate it if you could help me.
I wish to plot the following function against the variable X, but to do this, first I ...
1
vote
1answer
81 views
Mathematica can't integrate my function [closed]
I was trying to calculate the definite integral
$$
\int_0^.0076\int_0^.0425\int_0^.1275\frac{1}{x^2+y^2+z^2}\,dz\,dy\,dx
$$
I entered this:
...
3
votes
2answers
32 views
How to use an imported table data in a calculation of f[x,y,z], where each row of the column correspond to x,y,z? [duplicate]
I have a table with desired inputs of a given function efvc[n,m,u]. I want to calculate for different values of n, ...
0
votes
3answers
91 views
Integration involving Bessel function and algebraic function
While trying to compute the following integrals, Mathematica is not able to do that. Any suggestion will be helpful.
...
0
votes
0answers
38 views
Analytic derivatives of LegendreP[a, z] w.r.t. a at a = 0?
I am interested in finding analytic expressions for various derivatives of the LegendreP[a,z] w.r.t. a at ...
4
votes
1answer
78 views
Tips for Complicated Indefinite Integrals
I would like to have an analytical expression for some complicated indefinite integrals (example below). I am able to solve these integrals numerically, and I am able to plot them in Mathematica, ...
0
votes
1answer
40 views
Replacing one of the integrals in the multiple integral with an analytical solution
Problem consist in simplifying complicated multiple numerical integral, where I know analytical solution for a subset of them. Integrand is of the form
...
3
votes
1answer
205 views
How can I solve the limit by mathematica?
I use the Limit and DiscreteLimit to solve it but failed. How to solve it by Mathematica?
$$\underset{n\to \infty }{\text{lim}}n ...
1
vote
1answer
51 views
How to apply NIntegrate three times
I have following integration.
$$I=\int_{0}^{\frac{\pi}{2}} \int_{0}^{\infty}
\gamma e^{- \lambda \left(\gamma^2+2d\gamma\cos\theta -d^2 + \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} 2d\cos\Theta(d\cos\...
5
votes
1answer
82 views
Confusion in finding the definite integral
So, I'm new to Mathematica. I tried evaluating the following definite integral. However the answer i get from wolfram alpha & mathematica are different.
Can someone please point out what I'm ...
2
votes
1answer
52 views
Taking a derivative of an eigenvector
I'm trying to calculate the derivative of an eigenvector that I obtain by
...
0
votes
3answers
119 views
Assuming $ f(x) = 1/\ln(x) $, plot $ \int f(x) \mathrm dx $ on (1, 5) [closed]
Assume $ f(x) = 1/\ln(x) $. Plot $ \int f(x) \mathrm dx $ on (1, 5)
How can I make a plot even though $ x=1 $ could be zero in the denominator?
