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