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Module « scipy.special »

Fonction psi - module scipy.special

Signature de la fonction psi

def psi(*args, **kwargs) 

Description

help(scipy.special.psi)

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


    psi(z, out=None)

    The digamma function.

    The logarithmic derivative of the gamma function evaluated at ``z``.

    Parameters
    ----------
    z : array_like
        Real or complex argument.
    out : ndarray, optional
        Array for the computed values of ``psi``.

    Returns
    -------
    digamma : scalar or ndarray
        Computed values of ``psi``.

    Notes
    -----
    For large values not close to the negative real axis, ``psi`` is
    computed using the asymptotic series (5.11.2) from [1]_. For small
    arguments not close to the negative real axis, the recurrence
    relation (5.5.2) from [1]_ is used until the argument is large
    enough to use the asymptotic series. For values close to the
    negative real axis, the reflection formula (5.5.4) from [1]_ is
    used first. Note that ``psi`` has a family of zeros on the
    negative real axis which occur between the poles at nonpositive
    integers. Around the zeros the reflection formula suffers from
    cancellation and the implementation loses precision. The sole
    positive zero and the first negative zero, however, are handled
    separately by precomputing series expansions using [2]_, so the
    function should maintain full accuracy around the origin.

    References
    ----------
    .. [1] NIST Digital Library of Mathematical Functions
           https://dlmf.nist.gov/5
    .. [2] Fredrik Johansson and others.
           "mpmath: a Python library for arbitrary-precision floating-point arithmetic"
           (Version 0.19) http://mpmath.org/

    Examples
    --------
    >>> from scipy.special import psi
    >>> z = 3 + 4j
    >>> psi(z)
    (1.55035981733341+1.0105022091860445j)

    Verify psi(z) = psi(z + 1) - 1/z:

    >>> psi(z + 1) - 1/z
    (1.55035981733341+1.0105022091860445j)
    

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