Module « scipy.special »

Fonction ellipj - module scipy.special

Signature de la fonction ellipj

Description

ellipj.__doc__

ellipj(x1, x2[, out1, out2, out3, out4], / [, out=(None, None, None, None)], *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

ellipj(u, m)

Jacobian elliptic functions

Calculates the Jacobian elliptic functions of parameter `m` between
0 and 1, and real argument `u`.

Parameters
----------
m : array_like
    Parameter.
u : array_like
    Argument.

Returns
-------
sn, cn, dn, ph : ndarrays
    The returned functions::

        sn(u|m), cn(u|m), dn(u|m)

    The value `ph` is such that if `u = ellipkinc(ph, m)`,
    then `sn(u|m) = sin(ph)` and `cn(u|m) = cos(ph)`.

Notes
-----
Wrapper for the Cephes [1]_ routine `ellpj`.

These functions are periodic, with quarter-period on the real axis
equal to the complete elliptic integral `ellipk(m)`.

Relation to incomplete elliptic integral: If `u = ellipkinc(phi,m)`, then
`sn(u|m) = sin(phi)`, and `cn(u|m) = cos(phi)`. The `phi` is called
the amplitude of `u`.

Computation is by means of the arithmetic-geometric mean algorithm,
except when `m` is within 1e-9 of 0 or 1. In the latter case with `m`
close to 1, the approximation applies only for `phi < pi/2`.

See also
--------
ellipk : Complete elliptic integral of the first kind
ellipkinc : Incomplete elliptic integral of the first kind

References
----------
.. [1] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/