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SciPy

This is documentation for an old release of SciPy (version 0.18.1). Read this page in the documentation of the latest stable release (version 1.15.1).

scipy.special.yv

scipy.special.yv(v, z) = <ufunc 'yv'>

Bessel function of the second kind of real order and complex argument.

Parameters:

v : array_like

Order (float).

z : array_like

Argument (float or complex).

Returns:

Y : ndarray

Value of the Bessel function of the second kind, Yv(x).

See also

yve
Yv with leading exponential behavior stripped off.

Notes

For positive v values, the computation is carried out using the AMOS [R482] zbesy routine, which exploits the connection to the Hankel Bessel functions H(1)v and H(2)v,

Yv(z)=12ı(H(1)vH(2)v).

For negative v values the formula,

Yv(z)=Yv(z)cos(πv)+Jv(z)sin(πv)

is used, where Jv(z) is the Bessel function of the first kind, computed using the AMOS routine zbesj. Note that the second term is exactly zero for integer v; to improve accuracy the second term is explicitly omitted for v values such that v = floor(v).

References

[R482](1, 2) Donald E. Amos, “AMOS, A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order”, http://netlib.org/amos/

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