# 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
varray_like

Order of the Struve function (float).

xarray_like

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

Returns
Hndarray

Value of the Struve function of order v at x.

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