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
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.

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(1,2)

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

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