# Tagged Questions

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### Simulation of Parabolic Cylinder Function $U(a,x)$ for complex arguments

According to Wolfram Mathworld $U(a,x) = D_{-a-1/2} (x),$ and $D_v(z) = 2^{v/2}e^{-z^2/4}U(-\frac{1}{2}v, \frac{1}{2}, \frac{1}{2}z^2)$, Using the GNU Scientific Library (GSL) it seems possible ...
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### Numerical computation of the complex elliptic integral $E(k)$ for medium $|k|$

I have implemented Carlson's algorithm for $E(k)$ from Numerical computation of real or complex elliptic integrals (available from ArXiv eprint, see also DLMF). It is essentially his formula (46) ...
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### Interpolation with the roots of orthogonal polynomials & Spectral expansion

I'm a bit confused about the relationships between these two approximation methods mentioned in the title. Does this kind of interpolation also belongs to the field of spectral methods? Are the ...
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### I am searching for c++ code of the complex polygamma function

I googled about some code on the complex polygamma function especially c++ code, but can't find anything. Does anyone know where to find such code? The complex digamma function does exist but not the ...
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### Python Vectorizing a Function Returning an Array

I have the following function that has been vectorized so that for every element in input array t, an array is output: ...
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### How do I develop numerical routines for the evaluation of my own special functions?

This question was previously posted to Math.SE here and had received no answers at the time of this posting. When performing computational work, I often come across a univariate function, defined in ...
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### Appell function implementation in C++?

Is there a C++/C implementation of the Appell series? GSL and Boost do not seem to have this function.
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### Second derivative of the Associated Legendre functions

I would like to compute, as part of the solution of the Laplace equation using the Fast Multipole Method, the second derivative of the associated legendre functions of the first kind . Specifically, I ...
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### Efficient computation of tangent of fraction of angle

I want to compute $a = \tan(f \theta)$ for $f\in [0,1]$, given $g = \tan\theta$. Obviously, I can compute $a = \tan(f\tan^{-1}g)$, but I'm wondering if there's a more efficient way that avoids having ...
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### How to use polylogarithm function in c++?

Is there any preprocessor directives that could be used to use the polylog function? Or is it included in cmath? If so, do you call it by Li or by polylog? EDIT: What I really am trying to do is ...
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### Evaluate the sum

I want to evaluate the sum $$\sum_{k=1}^\infty \left(\frac{i+1}{\sqrt{2}}\right)^k\cdot k^{-\alpha}$$ where $i=\sqrt{-1}$ and $\alpha\in[\frac{3}{4},1]$ with 8 digits accuracy. If I am willing to ...
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### Does transforming $J_0(x)\to\int\cos(x\sin\theta)$ help with numerical integration?

I've heard anecdotally that when one is trying to numerically do an integral of the form $$\int_0^\infty f(x) J_0(x)\,\mathrm{d}x$$ with $f(x)$ smooth and well-behaved (e.g. not itself highly ...
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