Questions tagged [special-functions]

Questions on the special mathematical functions implemented in Mathematica.

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Using NDSolve on the Painlevé equations

In an earlier question of mine, I was looking for a way to handle certain kinds of singularities (poles) when using NDSolve. Michael E2's answer, which relied on ...
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Generalized Lambert W Function?

The Lambert W Function (defined as the inverse of $x e^x$) is implemented in Mathematica as ProductLog. Has anyone made any progress implementing the Generalized Lambert W Function defined as the ...
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Abnormally long computation time using AppellF1 function

I am trying to use the AppellF1 function in Mathematica 13.3.1 on an Ubuntu machine with an i7 13700. The inbuilt function seems to be much slower in some cases ...
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What is the exact formula Mathematica uses for Riemann zeta function? [closed]

I'm trying to find the formula of the zeta function used to plot this graph: This is taken from Wikipedia Riemann Zeta Function. It was created in Mathematica by ...
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Plot of a complicated function under double summation

I wrote the following inputs in mathematica to plot the following expression: ...
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How to compile inverse error function?

I have the following code: ...
1 vote
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Strange behavior of error function series expansion at infinity

Evaluating Normal[Series[1/ (1 + xi Erf[xi]), {xi, ∞, 2}]] Normal[Series[1/( xi (1/xi + Erf[xi])), {xi, ∞, 2}]] gives ...
1 vote
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A request on the kernel of the function ”SpheroidalEigenvalue“ in Mathemitica 11

I want to understand the algorithm of the function "SpheroidalEigenvlaue" in Mathematica 11, especially the code of the following command. Then I will try to use this algorithm to reproduce ...
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HypExp and HPL packages for hypergeometric functions: Evaluating a function HPL[{minus,plus},x]?

I am currently using the HypExp and HPL packages, which are useful for expanding hypergeometric functions in series around integer or half-integer values, as in common in dimensional regularization ...
1 vote
TLDR: How to expand gamma functions or Pochammer symbols in an arbitrarily long product? Some context I am trying to find out a closed-form expression for $\langle r^\alpha\rangle$ for the non-...