SciPy

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 [R494] 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

[R494](1, 2) NIST Digital Library of Mathematical Functions http://dlmf.nist.gov/11