Questions on the special mathematical functions implemented in Mathematica.
10
votes
6answers
2k views
About multi-root search in Mathematica for transcendental equations
I have some questions for multiroot search for transcendental equations. Is there any clever solution to find all the roots for a transcendental equation in a specific range?
Perhaps ...
6
votes
2answers
400 views
28
votes
2answers
916 views
What is the difference between a few simplification techniques?
I am trying to understand the difference between Refine, Simplify and FullSimplify, and when ...
7
votes
3answers
446 views
Checking if the roots of a function are real
I'm trying to determine if the roots of a function are real. How would you do that?
(In particular I'm interested in verifying that the roots of LegendreP[6, x] ...
7
votes
4answers
436 views
Finding the roots of Hypergeometric1F1[]
I am trying to find the roots, λ, for this equation:
Hypergeometric1F1[1/4 (2 - λ /β), n + 1, β]
for certain ...
6
votes
1answer
414 views
Hankel Transform integrals won't work in Mathematica
I'm trying to do this integral, which is shown on the Wikipedia page on the Hankel transformation:
$$\int_0^{2\pi}\mathrm d\varphi\;e^{\mathrm im\varphi}e^{\mathrm ikr\cos(\varphi)}$$
The answer is ...
16
votes
1answer
274 views
Peirce's quincuncial projection
The Peirce quincuncial projection is the cartographic projection of a sphere onto a square.
In short, I would like to see it implemented in Mathematica.
Here is my code:
...
12
votes
2answers
365 views
Visualizing vector spherical harmonics
I have painstakingly derived the vector-spherical harmonics $\mathbf{V}_{J,\,M}^\ell(\theta, \phi)$, which are the generalization of ordinary spherical harmonics $Y_\ell^m(\theta, \phi)$ to vector ...
8
votes
1answer
465 views
solve an integral equation numerically
I am trying to find a numerical solution for an equation of the form:
$$
f(t)=\int_{t_{min}}^{t} {\exp[2 (t^\prime - t)] E(t^\prime) f(t^\prime)}
+ \int_{t}^{0}{ \exp(t^\prime - t) E(t^\prime) ...
10
votes
4answers
691 views
Numerical underflow for a scaled error function
I calculate scaled error function defined as
f[x_] := Erfc[x]*Exp[x^2]
but it can not calculate f[30000.]. ...
0
votes
2answers
198 views
Using Mathematica to find poles of Gamma functions [closed]
I am concerned about the expression on the RHS of equation A.5 (page 19) in this paper:
$$\int\frac{d^d ...
7
votes
2answers
525 views
problem with coloring spherical harmonics
I want to color a spherical harmonics. So I write as follows.
...
3
votes
2answers
216 views
1
vote
1answer
169 views
Plotting Fresnel function
I am trying to plot the partial sums and the cesaro means of the function $\sqrt{|x|}$ and for $a_{n}$, I obtained the following code which contains FresnelS.
...
