Unanswered Questions
290 questions with no upvoted or accepted answers
49
votes
0
answers
3k
views
Fast Spherical Harmonics radiative transfer
This is a rather specific question and I apologize for spamming you with some lengthy code. But it could be interesting for some reader and maybe you can help out, so please bear with me.
I am using ...
- 141
11
votes
0
answers
374
views
MacDonald formula for Modified Bessel Functions
How can I make Mathematica understand these two integrals?
$$\int_0^{\infty} e^{-x \cosh{\xi}} d\xi = K_0(x)$$
$$\int_0^{\infty} e^{-\frac{1}{2} \Big( \frac{x y}{u} + u \frac{x^2+y^2}{x y} \Big) } K_{...
CommunityBot
- 1
10
votes
0
answers
211
views
Bug in SumConvergence
Bug introduced in 10.0.1 and fixed in 12.0.0
Version 11.2.0.0 on MacBook Pro:
...
- 13.7k
8
votes
2
answers
1k
views
Spherical harmonics and Laplace operator
The spherical harmonic function $Y_l^m(\theta,\phi)$ is defined to be an eigenfunction of the angular part of the Laplace operator with eigenvalue $-l(l+1)$. In other words, it solves the PDE:
$$\...
CommunityBot
- 1
8
votes
0
answers
2k
views
Inverse Laplace transform not obtained
I can't seem to be able to compute the inverse Laplace transform of a Laplace transform:
...
- 33.5k
7
votes
0
answers
235
views
Buggy behavior of EllipticE[0,k] with arbitrary precision input
Bug introduced in 13.2 or earlier.
I am having an issue where if I provide the EllipticE function with a first argument of zero and a second argument with a precision lower than that of machine ...
- 17.2k
7
votes
0
answers
128
views
Dedekind Zeta Function in Mathematica (at least for quadratic number field)
Does there exist some way to use Mathematica to compute the Dedekind Zeta function for an arbitrary algebraic number field? Or does there exist some package to do this?
I am actually only interested ...
- 191
7
votes
0
answers
201
views
SiegelTheta gives misleading message when the dimensions don't match
Bug introduced in 6.0 and persisting through 13.2.0
SiegelTheta is new in 6.0
In order to test the SiegelTheta function, I ...
- 17.2k
7
votes
0
answers
597
views
Reproducing the Integral Definition of the Modified Bessel function
I need to simplify some integral expressions in terms of special functions, such as the modified Bessel function of the first kind. See for example Eq. (5) on this page. Notice that the real ...
- 66.4k
6
votes
0
answers
248
views
Bugs in hypergeometric functions with negative integer lower parameters
Bug introduced in 13.0 or earlier and persisting through 13.2.0 or later.
If you were to evaluate these expressions, Mathematica returns the value shown.
...
- 17.2k
6
votes
0
answers
154
views
AppellF1 calculation hangs indefinitely
The built-in AppellF1 function seems generally useless. For example,
AppellF1[3/4, 1/2, 1/2, 7/4, (7 + 4 Sqrt[3]), (7 - 4 Sqrt[3])]
hangs indefinitely on my system....
6
votes
0
answers
101
views
What makes ListPlot better than N?
I wanted to numerically verify the validity of the formula for the first Stieltjes constant
$$\gamma_1=-\frac12\sum_{n=0}^\infty\frac1{n+1}\sum_{k=0}^n\binom{n}{k}(-1)^k\log^2(k+1)$$
...
- 10.1k
6
votes
0
answers
298
views
Why doesn't Log[Gamma[]] simplify to LogGamma[] where it could?
I have been playing with various equations involving amount of permutations in relatively large sets. Easiest way to look at these is something like Log[10, bignumber!] . Often expressions, even ...
5
votes
0
answers
249
views
Hypergeometric Function Integration Using Mellin-Barnes Representation
I have the following integral:
$$
I=\int_0^1 d \alpha d \beta d \gamma r(\gamma) s(\alpha, \beta) T(\alpha, \beta, \gamma)
$$
where I define
$$r(\gamma)=(\gamma(1-\gamma))^{ -1 / 2+\epsilon / 2}$$
and,...
- 139
5
votes
0
answers
252
views
Possible bug with EllipticPi
I am calculating the incomplete elliptic integral of the third kind in Mathematica 11.3 using EllipticPi. Since my range of phi ...
- 239k