# scipy.special.riccati_jn

scipy.special.riccati_jn(n, x)

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

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

  This function computes the value and first derivative of the Ricatti-Bessel 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
    jn ndarray

      Value of j0(x), …, jn(x)

    jnp ndarray

      First derivative j0’(x), …, jn’(x)

  Notes

  The computation is carried out via backward 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/f_src/special_functions/special_functions.html

  2

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

scipy.special.spherical_kn scipy.special.riccati_yn