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# scipy.special.riccati_yn

scipy.special.riccati_yn(n, x)

  Compute Ricatti-Bessel function of the second kind and its derivative.

  The Ricatti-Bessel function of the second kind is defined as \(x y_n(x)\), where \(y_n\) is the spherical Bessel function of the second kind of order \(n\).

  This function computes the value and first derivative of the function for all orders up to and including n.

  Parameters:
    n int

      Maximum order of function to compute

    x float

      Argument at which to evaluate

  Returns:
    yn ndarray

      Value of y0(x), …, yn(x)

    ynp ndarray

      First derivative y0’(x), …, yn’(x)

  Notes

  The computation is carried out via ascending recurrence, using the relation DLMF 10.51.1 [2].

  Wrapper for a Fortran routine created by Shanjie Zhang and Jianming Jin [1].

  References

  [1]

  Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html

  [2]

  NIST Digital Library of Mathematical Functions. https://dlmf.nist.gov/10.51.E1