Module « scipy.special »

Fonction sici - module scipy.special

Signature de la fonction sici

Description

sici.__doc__

sici(x[, out1, out2], / [, out=(None, None)], *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

sici(x, out=None)

Sine and cosine integrals.

The sine integral is

.. math::

  \int_0^x \frac{\sin{t}}{t}dt

and the cosine integral is

.. math::

  \gamma + \log(x) + \int_0^x \frac{\cos{t} - 1}{t}dt

where :math:`\gamma` is Euler's constant and :math:`\log` is the
principle branch of the logarithm.

Parameters
----------
x : array_like
    Real or complex points at which to compute the sine and cosine
    integrals.

Returns
-------
si : ndarray
    Sine integral at ``x``
ci : ndarray
    Cosine integral at ``x``

Notes
-----
For real arguments with ``x < 0``, ``ci`` is the real part of the
cosine integral. For such points ``ci(x)`` and ``ci(x + 0j)``
differ by a factor of ``1j*pi``.

For real arguments the function is computed by calling Cephes'
[1]_ *sici* routine. For complex arguments the algorithm is based
on Mpmath's [2]_ *si* and *ci* routines.

References
----------
.. [1] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/
.. [2] Fredrik Johansson and others.
       "mpmath: a Python library for arbitrary-precision floating-point arithmetic"
       (Version 0.19) http://mpmath.org/