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# 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, \(Y_v(x)\).

  See also

  `yve`
    \(Y_v\) with leading exponential behavior stripped off.

  Notes

  For positive v values, the computation is carried out using the AMOS [R543] 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

  [R543] | (1, 2) Donald E. Amos, “AMOS, A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order”, http://netlib.org/amos/