SciPy

scipy.special.y0

scipy.special.y0(x) = <ufunc 'y0'>

Bessel function of the second kind of order 0.

Parameters:

x : array_like

Argument (float).

Returns:

Y : ndarray

Value of the Bessel function of the second kind of order 0 at x.

See also

j0, yv

Notes

The domain is divided into the intervals [0, 5] and (5, infinity). In the first interval a rational approximation \(R(x)\) is employed to compute,

\[Y_0(x) = R(x) + \frac{2 \log(x) J_0(x)}{\pi},\]

where \(J_0\) is the Bessel function of the first kind of order 0.

In the second interval, the Hankel asymptotic expansion is employed with two rational functions of degree 6/6 and 7/7.

This function is a wrapper for the Cephes [R496] routine y0.

References

[R496](1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html

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