scipy.special.yv¶
-
scipy.special.yv(v, z) = <ufunc 'yv'>¶ Bessel function of the second kind of real order and complex argument.
- Parameters
- varray_like
Order (float).
- zarray_like
Argument (float or complex).
- Returns
- Yndarray
Value of the Bessel function of the second kind, \(Y_v(x)\).
See also
yve\(Y_v\) with leading exponential behavior stripped off.
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/