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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).
Returns: Y : ndarray
Value of the exponentially scaled Bessel function.
Notes
For positive v values, the computation is carried out using the AMOS [R483] zbesy routine, which exploits the connection to the Hankel Bessel functions H(1)v and H(2)v,
Yv(z)=12ı(H(1)v−H(2)v).For negative v values the formula,
Y−v(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
[R483] (1, 2) Donald E. Amos, “AMOS, A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order”, http://netlib.org/amos/