# scipy.special.struve

scipy.special.struve(v, x) = <ufunc 'struve'>

  Struve function.

  Return the value of the Struve function of order v at x. The Struve function is defined as,

  \[H_v(x) = (z/2)^{v + 1} \sum_{n=0}^\infty \frac{(-1)^n (z/2)^{2n}}{\Gamma(n + \frac{3}{2}) \Gamma(n + v + \frac{3}{2})},\]

  where \(\Gamma\) is the gamma function.

  Parameters
    v array_like

      Order of the Struve function (float).

    x array_like

      Argument of the Struve function (float; must be positive unless v is an integer).

  Returns
    H ndarray

      Value of the Struve function of order v at x.

  See also

  `modstruve`

  Notes

  Three methods discussed in [1] are used to evaluate the Struve function:

  - power series

  - expansion in Bessel functions (if \(|z| < |v| + 20\))

  - asymptotic large-z expansion (if \(z \geq 0.7v + 12\))

  Rounding errors are estimated based on the largest terms in the sums, and the result associated with the smallest error is returned.

  References

  1

    NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/11

scipy.special.riccati_yn scipy.special.modstruve