# Questions tagged [special-functions]

Questions on the special mathematical functions implemented in Mathematica.

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### expansion of hypergeometric series [closed]

I am completely new to mathematica. I am not sure how to calculate the expression 2F1. Is it possible to a closed form solution in terms of z of the hypergeometric series 2F1(-a, N/2-a, N/2; z) and ...
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### Adding a module to teach Mathematica the Laplace transform of particular Mittag-Leffler functions

Mathematica 11.3 is not aware of a useful Laplace transform LaplaceTransform[t^(-a) MittagLefflerE[a, a, t^a], t, s] which for ...
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### Plotting a Legendre Polynomial

currently I am trying to plot for the Legendre polynomial $P_n(x)$ for $n=0,1,2,3,4$ and $-1 \leq x \leq 1$ . To plot for it, I wrote the following code: ...
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### Why does Integrate get this wrong?

Why does Integrate get this wrong? ...
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### Exact value involving ProductLog

By manual manipulation, it's not too difficult to show that the value of the following expression is exactly $1.$ How to convince Mathematica to do the simplification? ...
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### Precompute Functions for use in NDSolve [closed]

I have a very complicated pair of functions $F(x,y), G(x,y)$ that are used in a differential equation $0 = x'' + F(x,y)$, $0 =y '' + G(x,y)\,.$ $F$ and $G$ are roughly sums of products of the Bessel ...
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### Error in Creating Orthogonal Polynomials

I'm trying to create my own set of polynomials orthogonal to weight $w(x)=x^{14}$ on $[-a,a]$. My code: ...
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### How to Integrate this expression?

All the parameters ($r, b,$ and $q$) are real and positive. Is it possible to do the below integration? ...
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### How to DSolve this differential equation?

How can I find h[r] from this equation? I need h[r] or its r derivative. ...
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### Non-Convergence In Creating Legendre Series

I'm trying to use Mathematica to create a Legendre-Fourier series using this Wikipedia article. Here is my code: ...
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### Understanding the output of a calculation

I have a simple question about the output of a calculation. I have written a function which is a sum of 3j-symbols and Clebsch-Gordan coefficients in which I sum over various indices. ...
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### Strange behaviour with EllipticTheta functions

For some time I have been using EllipticTheta[3,-,-] functions, and to me it seems that Mathematica is really not handling them in the best way. Below are two of ...
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### When is a symbol a Symbol? Is there an easy Mathematica way to test if an object is a symbol sort of like a SymbolQ?

Yes I know there is no built-in native function called SymbolQ (but JavaScript does). However, could one be simulated to work for most cases? I often rely on ...
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### Code that produces plot in V5 doesn't work in later versions

I have problem in plotting Integral function. I can compute/plot the graph of this integration below in Mathematica 5.0, but it is not possible to plot it in higher Mathematica versions. My code is: <...
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### Problems with Erf for large arguments with small imaginary part [closed]

While performing some higher precision calculation, I noticed that Mathematica 12.1 killed the kernel and cleared all prior definitions. The problem was with Erf ...