CnOCRService/Lib/site-packages/sympy/series/series.py

from sympy.core.sympify import sympify


def series(expr, x=None, x0=0, n=6, dir="+"):
    """Series expansion of expr around point `x = x0`.

    Parameters
    ==========

    expr : Expression
           The expression whose series is to be expanded.

    x : Symbol
        It is the variable of the expression to be calculated.

    x0 : Value
         The value around which ``x`` is calculated. Can be any value
         from ``-oo`` to ``oo``.

    n : Value
        The number of terms upto which the series is to be expanded.

    dir : String, optional
          The series-expansion can be bi-directional. If ``dir="+"``,
          then (x->x0+). If ``dir="-", then (x->x0-). For infinite
          ``x0`` (``oo`` or ``-oo``), the ``dir`` argument is determined
          from the direction of the infinity (i.e., ``dir="-"`` for
          ``oo``).

    Examples
    ========

    >>> from sympy import series, tan, oo
    >>> from sympy.abc import x
    >>> f = tan(x)
    >>> series(f, x, 2, 6, "+")
    tan(2) + (1 + tan(2)**2)*(x - 2) + (x - 2)**2*(tan(2)**3 + tan(2)) +
    (x - 2)**3*(1/3 + 4*tan(2)**2/3 + tan(2)**4) + (x - 2)**4*(tan(2)**5 +
    5*tan(2)**3/3 + 2*tan(2)/3) + (x - 2)**5*(2/15 + 17*tan(2)**2/15 +
    2*tan(2)**4 + tan(2)**6) + O((x - 2)**6, (x, 2))

    >>> series(f, x, 2, 3, "-")
    tan(2) + (2 - x)*(-tan(2)**2 - 1) + (2 - x)**2*(tan(2)**3 + tan(2))
    + O((x - 2)**3, (x, 2))

    >>> series(f, x, 2, oo, "+")
    Traceback (most recent call last):
    ...
    TypeError: 'Infinity' object cannot be interpreted as an integer

    Returns
    =======

    Expr
        Series expansion of the expression about x0

    See Also
    ========

    sympy.core.expr.Expr.series: See the docstring of Expr.series() for complete details of this wrapper.
    """
    expr = sympify(expr)
    return expr.series(x, x0, n, dir)