# Questions tagged [special-functions]

Questions on the special mathematical functions implemented in Mathematica.

1,167 questions
Filter by
Sorted by
Tagged with
179 views

### Is there a built-in for "circle function"?

Is there a built-in function in Mathematica for this function? \begin{equation} {\displaystyle \operatorname {Circ} (r)=\left\{{\begin{array}{rl}1,&{\text{if }}r<{1}\\{\frac {1}{2}},&{\text{...
62 views

71 views

### How to do a fast numerical computation of an oscillatory integral including HeunC function using Mathematica?

I am trying to numerically compute the following integral in Mathematica ...
96 views

### Computing the sign of an expression

Can you please help with the following. I would like to compute the sign of an expression: ...
310 views

### why do these two Meijer G functions not cancel each other?

I encountered such expressions in Mathematica MeijerG[{{ }, {1, c + 1/2}}, {{0, c, c, c}, { }}, 1] + MeijerG[{{1}, {c + 1/2}}, {{c, c, c}, {0}}, 1] which in ...
67 views

### Too small to represent and Chop in inaccessible algorithm

Overview I want to apply a specified Chop function to every step in an function call in Mathematica (in my case LegendreP), ...
73 views

### Convert GiNaC harmonic polylogarithms to HPL packages' notation in Mathematica

A general output from GiNaC (https://www.ginac.de/) of harmonic polylogarithms is H(a,b,c...,x). We want to convert it to Mathematica format (https://www.physik....
61 views

### Plotting Radiation Pattern for Hermite-Gaussian beams for different modes

I want to plot the Radiation Pattern for Hermite-Gaussian beams (HG beam) as given in the Figures Ref Research Paper Fig 2, where u and v be the beam modes for the Hermite-Gaussian beams The coding ...
68 views

### How to simplifying the following integral that involves Bessel functions and Exponential integral function?

I have obtained the following as a solution of heat conduction equation of a semi-infinite model in cylindrical coordinates which is initially subject to non-homogenous initial condition and isolated ...
88 views

### How to simplify the following integral to be in terms of Bessel functions?

I have evaluated the following integration using Mathematica. I obtained a solution in terms of Meijer G function. I wonder if it can be simplified to be in terms of Bessel functions. ...
52 views

### How to evaluate the following integrals using Mathematica?

I have the following integrals obtained during solving heat diffusion equation for semi-infinite system that is subject to non-homogenous initial condition in Laplace domain. I want to simplify the ...
229 views

### How to prove the following integration identity?

I have the following integration that I want to evaluate it using Mathematica. ...
I think Can be simplified to $-x^2$ I tried Reduce, FullSimplify, FunctionExpand, and ...