SciPy

scipy.special.modstruve

scipy.special.modstruve(v, x) = <ufunc 'modstruve'>

Modified Struve function.

Return the value of the modified Struve function of order v at x. The modified Struve function is defined as,

\[L_v(x) = -\imath \exp(-\pi\imath v/2) H_v(x),\]

where \(H_v\) is the Struve function.

Parameters
varray_like

Order of the modified Struve function (float).

xarray_like

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

Returns
Lndarray

Value of the modified Struve function of order v at x.

See also

struve

Notes

Three methods discussed in [1] are used to evaluate the 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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