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Newest 'special-functions' Questions - Mathematica Stack Exchange
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Learn more about TeamsQuestions tagged [special-functions]
Questions on the special mathematical functions implemented in Mathematica.
1,528 questions
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1
vote
1
answer
68
views
Help validating the solution to a nonlinear ODE: Does it solves other non-linear ODEs too? [closed]
I am working right now in this another question by doing examples and I got stuck in proving the results I found through Wolfram-Alpha are right.
The main differential equation is the following ODE:
$$...
3
votes
2
answers
119
views
Expanding the HypergeometricPFQ function gives complex values
I have a function
HypergeometricPFQ[{}, {2, 2}, -Log[n]]
which for real n > 0 gives a real values, as can be seen on the ...
0
votes
0
answers
48
views
How to improve the Mathematica implementations of q-Bessel polynomial?
I know Mathematica has implemented some QFunctions.
I have found this literature: q-Bessel polynomials, q-Laguerre polynomials, q-Charlier polynomials, etc.?
I have implemented q-Bessel polynomials in ...
1
vote
1
answer
88
views
Using `JacobiP` to approximate `BetaDistribution[a,b]`
I'm looking at generalized moment expansions of BetaDistribution. Below is an example using ChebychevT, I'm looking for help extending this to cover the general ...
1
vote
0
answers
23
views
0
votes
0
answers
93
views
Integrating Hypergeometric2F1 with large arguments
I am trying to integrate a function which contains two hypergeometric functions ${}_2F_{1}(a,b,c,z)$. In my particular case,
\begin{align}
a &= 1 + \ell - n,\\
b &= 1 + \ell + i \lambda x,\\
...
3
votes
1
answer
208
views
Demonstrating integral result involving Bessel function
On my laptop Mathematica does not take very long to determine that $\int_0^{\infty } \frac{\left(1-\exp \left(-a x^2\right)\right) J_0(b x)}{x} \, dx$ is equivalent to $\frac{1}{2} \Gamma \left(0,\...
1
vote
1
answer
221
views
How to speed up evaluation of a computationally expensive function?
The evaluation of the following code takes ages to finish:
...
1
vote
0
answers
46
views
Seek Mathematica implementation of q-analogs of Special functions
I know Mathematica has implemented some QFunctions.
What about Mathematica implementations of Elliptic gamma function, Hahn–Exton q-Bessel function, Jackson q-Bessel function,
q-exponential, q-gamma ...
6
votes
3
answers
723
views
Plotting spherical harmonics
I would like to recreate the following figure of spherical harmonics from Wikipedia.
I used the codes from Plotting real spherical harmonics with SphericalPlot3D, but the resulting spherical ...
0
votes
0
answers
100
views
How to properly use DirichletL?
I'm trying to construct in Mathematica the analytic continuation of the L-function associated with the number field Q(i). This was done, though opaquely, in the captivating YouTube series "RH ...
9
votes
3
answers
299
views
Obtaining symbolic series expansion of $(W_0(-z/e)+1)^{-1}$
Is there a way to massage Mathematica to give a symbolic expression for $s$th series coefficient of $(W_0(-z/e)+1)^{-1}$
...
2
votes
2
answers
199
views
FoxH function not working
I want to calculate the following Fox H-function:
$$
H^{1,1}_{1,2}
\left(
0.2
\,
\middle|
\begin{array}
\,
(-1, 1) \\
(-1, 1), \, (0, 0.5)
\end{array}
\right)
$$
So I tried ...
0
votes
0
answers
57
views
Conical functions with Imaginary argument
I am playing with a differential equation whose solutions are conical functions (Legendre functions with a complex order) with a pure imaginary argument
$
P_{i\nu -1/2}(i \sinh \xi)
$
or $Q_{i\nu -...
4
votes
0
answers
159
views
Why is Mathematica thinking that 1 is a variable?
I'm trying to solve an ODE and upon executing:
...
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