# Tagged Questions

Questions on the special mathematical functions implemented in Mathematica.

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### Calculating $\lim_{x\to 1} \, \int -\frac{i \text{Li}_2\left(x-x^2\right)}{\sqrt{3} \left(x-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)} \, dx$

How can we force Mathematica to compute this limit? $$\lim_{x\to 1} \, \int -\frac{i \text{Li}_2\left(x-x^2\right)}{\sqrt{3} \left(x-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)} \, dx$$ It seems it ...
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### Evaluating a Series expansion of PolyLog function

I am trying to evaluate an expansion of the following integral $$\int_0^\infty \frac{p^4}{1+\exp\left({\frac{p^2}{2mT} - \frac{\mu}{T}}\right)}\, dp = A_0(m,\mu) + A_2(m,\mu)T^2 + \ldots$$ in terms ...
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### Find all roots of a function with parabolic cylinder functions in a range of the variable

I want to find all roots of a function involving Parabolic Cylinder Functions. In what follows, I define 2 variables $\xi1$ and $\xi2$, which in turn depend on $\omega$. My function is then defined as ...
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### How to find and verify relationships between functions?

MMa gave me a complicated result involving Hypergeometric0F1's. It was much less complicated after I discovered this identity: ...
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### NSolve can not handle a PolyGamma equation

I would like to solve the following equations numerically: ...
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### Computing Poincaré symbolic solution for an arbitrary integer order polynomial

In the 1880s, Poincaré created functions which give the solution to the nth order polynomial equation in finite form. These functions turned out to be "natural" generalizations of the elliptic ...
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### FactorialPower and Factorial

After some computation, I have obtained a function FactorialPower[1, n, -1]. Clearly, FactorialPower[1, n, -1] equals ...
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### Plotting the Schwarz D minimal surface

With the aid of the following paper I'm trying to plot the Schwarz D minimal surface: paper. So far I have followed all the instructions to the best of my abilities and have come up with the following ...
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### Does Mathematica support Laguerre Polynomials of Matrix Argument? [duplicate]

I am wondering whether Mathematica can also compute the Laguerre polynomials of matrix argument as the appear in multivariate statistics? For example, they appear in this paper here: http://www.jstor....
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### NIntegrate and Integrate of a Spherical Bessel function

I am trying to integrate a spherical Bessel function. I have used both the Integrate and NIntegrate functions in Mathematica but ...
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### Probability of multivariate normal being positive on each coordinate

How can I find the probability that each coordinate of a specified multivariate normal distribution is positive? I tried the following, which I believed should work ...
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### Bug in associated Legendre Polynomials?

Mathematica's definition of the connection of associated Legendre polynomials with $m$ and $-m$ is: $P_l^{-m}=(-1)^m \frac{(l-m)!}{(l+m)!} P_l^m$. We also now that $|m|>l \Rightarrow P_l^m=0$. ...
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### EllipticF reduction

Is it possible to reduce the following Z to Legendre form Elliptic integral of the First kind? $$\int \dfrac {\sec u\; du } {\sqrt{ (1- {(\nu \tan u)}^2 }} ..(1*)$$ With ...
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### Compile a MeijerG function [duplicate]

I am not very experienced with Compile, I tried to use it for a Meijer-G function ...