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# 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). H : ndarray Value of the Struve function of order v at x.

Notes

Three methods discussed in [R532] 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

 [R532] (1, 2) NIST Digital Library of Mathematical Functions http://dlmf.nist.gov/11