# Questions tagged [special-functions]

Questions on the special mathematical functions implemented in Mathematica.

268 questions with no upvoted or accepted answers
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### 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 ...
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### 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....
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### What makes ListPlot better than N?

I wanted to numerically verify the validity of the formula for the first Stieltjes constant $$\gamma_1=-\frac12\sum_{n=0}^\infty\frac1{n+1}\sum_{k=0}^n\binom{n}{k}(-1)^k\log^2(k+1)$$ ...
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### 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 ...
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### 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 ...
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### Issues with the series expansion of Nielsen generalized polylogarithms in Mathematica 11.3

Bug introduced in 11.3. Fixed in 12.0. In Mathematica 9, 10.3 and 11.0 I can easily expand PolyLog[2, 2, x] around $x=1$ using ...
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### Integrating a product of three Spherical Harmonics

The following command is returned unevaluated. The answer is well known to be related to Wigner's 3j Symbol which is also a defined function in Mathematica. ...
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### Express special function (Hypergeometric1F1) in terms of another special function (HermiteH)

I have the following Mathematica expression: (2^k Gamma[1/2 + k] Hypergeometric1F1[-k, 1/2, t^2/2])/Sqrt[\[Pi]] where k is an integer and t is a real number, and ...
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### Integral Form of Modified Bessel Function of the Second Kind

Why can't Mathematica integrate r = Integrate[Exp[-x Cosh[t]], {t, 0, Infinity}]; r = Assuming[Element[x, Reals], Simplify[r]]; Together[r] From Wikipedia, it ...
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### Expansion of $E(i c \mid m)$ at $c\to\infty$?

Currently, I am using a Windows machine with Mathematica 8. I noticed a difference in a series expansion of the function EllipticE[] in comparison with a result ...
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### Why does an integer index inside a symbol become real when entering a ChebyshevT function with floating point arithmetic?

When I enter an indexed symbol into a ChebyshevT function with integer arithmetic like this: ChebyshevT[1, 3 * a[4]] I get the expected result: ...
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### Example in Help File does not evaluate as claimed

In the help file, under BellB, I read at "Properties and Relations": Sum can give results involving ...
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