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Computes the modified Bessel function of the second kind, \( K_n(x)=\frac{\Gamma(n+1/2)(2x)^n}{\sqrt\pi} \int_{0}^{\infty}\frac{\cos\tau} {(\tau^2+x^2)^{n+1/2}}\,\mathrm{d}\tau\).
It is the solution of \( x^{2}y''+xy'-(x^2+n^2)y=0\) for which \( y(0) = \infty\).
Defined in header
Parameters
n
: order of the function (non necessarily integral)x
: ordered floating argument.Return value
The value of \(\displaystyle K_n(x)=\frac{\Gamma(n+1/2)(2x)^n}{\sqrt\pi} \int_{0}^{\infty}\frac{\cos\tau}{(\tau^2+x^2)^{n+1/2}}\,\mathrm{d}\tau\) is returned.