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- 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)
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