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
- varray_like
Order (float).
- zarray_like
Argument (float or complex).
- Returns
- Yndarray
Value of the exponentially scaled Bessel function.
Notes
For positive v values, the computation is carried out using the AMOS [1] 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
- 1
Donald E. Amos, “AMOS, A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order”, http://netlib.org/amos/