All Questions
20 questions
6
votes
4
answers
510
views
Approximation of the Fabius function with a quotient of exponentials
Approximation of the Fabius function $f(x) = \text{FabiusF}[x+1]\cdot \text{HeavisideTheta}[1-x^2]$ - FabiusF[x] doesn't work in Wolfram-Alpha
I am looking to figure out how well the displaced version ...
- 175
0
votes
1
answer
49
views
EllipticPi argument is complex and can not be plotted. How to handle this problem?
inttau[r_]=-(1/Sqrt[0.0345106153943703 - ((37.3042 - r) (-25.578 + r) (62.8822 +
r))/(3000 r)])
This is my function of r, now I integrated it w r t r
...
- 175
0
votes
0
answers
33
views
Can't plot derivative of Hankel function [duplicate]
I am trying to plot the first derivative of $H^{(1)}_3 (ix)$ with respect to its argument $ix$, where $H^{(1)}_3 (ix)$ is the Hankel function of the first kind with order $3$, $x \in \mathbb{R}$ is a ...
- 315
4
votes
3
answers
306
views
Constant curvature surfaces. Revolution of the graphs of solutions to a nonlinear differential equation
I have the following differential equation:
$$\pi\cdot\text{y}(x)^2=\sqrt{1+\text{y}'(x)^2}\tag1$$
With the initial condition $\text{y}(0)=1$.
Now, I want to plot the solution in order to obtain the ...
- 2,021
4
votes
2
answers
396
views
Plotting the inverse function of a complicated function
So I have a function
F[x_] = Assuming[{Element[x, Reals], -1 < x < 1},
Integrate[1/Sqrt[(x^2 - 1)^2 + alpha*x], x]]
I'm now interested in the ...
- 1,285
-1
votes
1
answer
430
views
Plot fractional trigonometric functions with the Mittag-Leffler function
Can anyone help please?
Im trying to plot the solution $X$ of the system as in the paper attached - about fractional calculus which is
$X= [E_{\nu}(2t^{\nu})][2 \cos_{\nu}(3t^{\nu})+4 \sin_{\nu}(3t^{...
- 37
0
votes
1
answer
558
views
Plotting with the Mittag-Leffler function [closed]
I'm trying to plot the solution of fractional differential equations as shown in the photos below, The solutions are in terms of the Mittage-Leffler function, so I evaluated
...
- 37
2
votes
1
answer
90
views
Plot $g(r) = \int_0^\pi J_0(w\ r)\ \mathrm dw $
I want to plot $g(r) = \int_0^\pi J_0(w\ r)\ \mathrm dw $ 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 $w$.
- 23
2
votes
2
answers
220
views
Plot of partial derivative looks wrong and does not match the surface plot of the function
I have a function and I'm using Wolfram Cloud to analyze it.
F[p_, n_] := InverseBetaRegularized[0.1, p*n + 1, (1 - p)*n + 1]
When I plot the function, it looks ...
- 121
0
votes
1
answer
114
views
How do you find Si[x] has infinitely many values
How do you show that there are infinitely many values of $x$ such that $\operatorname{Si}(x)=a$ (where a is the horizontal asymptote, $a>0$). Find the least two (i.e. the closest to 0) of these $x$ ...
- 319
1
vote
2
answers
285
views
3
votes
2
answers
903
views
Nested Integrate and NIntegrate: Analytic and Numeric solutions?
Here is a function $F(r)$ which contains double integrations
$$F(r)=\exp\left[ \int_{0}^r dw \,\exp\left(-\int_{0}^w ds
\frac{s^2}{s^2+1} \left(1-\exp(- s)\right) \right) \right]$$
I am fine ...
- 207
3
votes
2
answers
330
views
Plot of Meijer-G function $g(t)$ disagrees with $\lim_{t\to \infty} g(t)$
My function is
$$g(t)=\frac{2}{\sqrt\pi t}-\frac{\pi t}{2}\,G_{0,3}^{3,0}\left(\frac{\pi^2 t^2}{4}\middle|-1,-\frac12,0\right)$$
where $G^{a,b}_{c,d}$ is the Meijer $G$ function. I want to know if $g(...
- 31
1
vote
1
answer
175
views
Plotting The derivative of the associated Legendre function [closed]
I was wondering why I was having difficulty plotting
∂[LegendreP[l, m, Cos[x]], x], where $l\in\mathbb{N}$ and $m\in\{-l,~-l+1,\cdots,l-1,~l\}$ as per usual for ...
- 149
16
votes
3
answers
1k
views
How do I numerically evaluate and plot the Fabius function?
The Fabius function is a well-known example in analysis of a non-analytic function that is infinitely differentiable. I want to be able to numerically evaluate the function for any real argument, as ...
- 161
11
votes
1
answer
418
views
Vastly incorrect answers obtained by increasing WorkingPrecision with modified Bessel functions
Bug introduced in 7.0 or earlier and fixed in 11.0
This is a follow-up to this question regarding numerical instabilities occurring with modified Bessel functions. In trying to explore J.M.'s answer ...
- 743
0
votes
1
answer
93
views
Plotting a function based on complicated integral
I have this function :
f[Lambda_] := K Integrate[x Exp[- x^2-Lambda x]
HypergeometricU[-Lambda,1/2,(x+ Lambda/2+2)^2],{x,0,Infinity}];
where
...
- 1
6
votes
2
answers
412
views
Imaginary terms in the derivative of Jacobi theta function (2) on the real line
I am trying to calculate/plot the derivative of the second Jacobi theta function $d\theta_2(0, e^{-\pi t} )/dt$.
Calculating or plotting the function itself works fine:
...
- 61
1
vote
2
answers
276
views
How to define a function that is related to derivative of Jacobi theta function
I would like to make 3D plot of the following function.
...
- 335
5
votes
1
answer
366
views
How to plot the result of this singular integral?
Please I open a new post here after this one : https://mathematica.stackexchange.com/a/59203/10158
Now I want to plot the function $f(a,b)$ as a function of $b$ for different values of $a$ : $a=0.5$ ,...
- 425