# scipy.special.yve¶

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

Exponentially scaled Bessel function of the second kind of real order.

Returns the exponentially scaled Bessel function of the second kind of real order v at complex z:

yve(v, z) = yv(v, z) * exp(-abs(z.imag))

Parameters: v : array_like Order (float). z : array_like Argument (float or complex). Y : ndarray Value of the exponentially scaled Bessel function.

Notes

For positive v values, the computation is carried out using the AMOS [R603] zbesy routine, which exploits the connection to the Hankel Bessel functions $$H_v^{(1)}$$ and $$H_v^{(2)}$$,

$Y_v(z) = \frac{1}{2\imath} (H_v^{(1)} - H_v^{(2)}).$

For negative v values the formula,

$Y_{-v}(z) = Y_v(z) \cos(\pi v) + J_v(z) \sin(\pi v)$

is used, where $$J_v(z)$$ 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

 [R603] (1, 2) Donald E. Amos, “AMOS, A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order”, http://netlib.org/amos/

scipy.special.yv

scipy.special.kn