scipy.special.struve¶
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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
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 http://dlmf.nist.gov/11