Module « scipy.special »

Fonction struve - module scipy.special

Signature de la fonction struve

Description

struve.__doc__

struve(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

struve(v, x)

Struve function.

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

.. math::
    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 :math:`\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`.

Notes
-----
Three methods discussed in [1]_ are used to evaluate the Struve function:

- power series
- expansion in Bessel functions (if :math:`|z| < |v| + 20`)
- asymptotic large-z expansion (if :math:`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.

See also
--------
modstruve

References
----------
.. [1] NIST Digital Library of Mathematical Functions
       https://dlmf.nist.gov/11