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Computes the modified Bessel functions of the first kind, \( I_{n}(x)=\left(\frac12z\right)^n\sum_{k=0}^{\infty}{\frac{(x^2/4)^k} {k!\,\Gamma (k+n +1)}}\).
It is the solution of \( x^{2}y''+xy'+(x^2-n^2)y=0\) for which \( y(0) = 0\).
Defined in header
Parameters
n
: order of the function (non necessarily integral),x
: ordered floating argument.Return value
The value of \(\displaystyle I_{n}(x)=\left(\frac12z\right)^n\sum_{k=0}^{\infty} {\frac{(x^2/4)^k}{k!\,\Gamma (k+n +1)}}\) is returned.