tmp/tmpzoy7ur37/{from.md → to.md}
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#### Cylindrical Neumann functions <a id="sf.cmath.cyl_neumann">[[sf.cmath.cyl_neumann]]</a>
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``` cpp
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double cyl_neumann(double nu, double x);
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float cyl_neumannf(float nu, float x);
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long double cyl_neumannl(long double nu, long double x);
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```
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*Effects:* These functions compute the cylindrical Neumann functions,
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also known as the cylindrical Bessel functions of the second kind, of
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their respective arguments `nu` and `x`.
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*Returns:* $$%
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\mathsf{N}_\nu(x) =
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\left\{
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\begin{array}{cl}
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\displaystyle
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\frac{\mathsf{J}_\nu(x) \cos \nu\pi - \mathsf{J}_{-\nu}(x)}
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{\sin \nu\pi },
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& \mbox{for $x \ge 0$ and non-integral $\nu$}
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\\
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\\
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\displaystyle
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\lim_{\mu \rightarrow \nu} \frac{\mathsf{J}_\mu(x) \cos \mu\pi - \mathsf{J}_{-\mu}(x)}
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{\sin \mu\pi },
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& \mbox{for $x \ge 0$ and integral $\nu$}
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\end{array}
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\right.$$ where $\nu$ is `nu` and x is `x`.
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*Remarks:* The effect of calling each of these functions is
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*implementation-defined* if `nu >= 128`.
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See also [[sf.cmath.cyl_bessel_j]].
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