Module « scipy.special »

Fonction shichi - module scipy.special

Signature de la fonction shichi

Description

shichi.__doc__

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

shichi(x, out=None)

Hyperbolic sine and cosine integrals.

The hyperbolic sine integral is

.. math::

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

and the hyperbolic cosine integral is

.. math::

  \gamma + \log(x) + \int_0^x \frac{\cosh{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 hyperbolic sine
    and cosine integrals.

Returns
-------
si : ndarray
    Hyperbolic sine integral at ``x``
ci : ndarray
    Hyperbolic cosine integral at ``x``

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

For real arguments the function is computed by calling Cephes'
[1]_ *shichi* routine. For complex arguments the algorithm is based
on Mpmath's [2]_ *shi* and *chi* 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/