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64 lines
1.8 KiB
64 lines
1.8 KiB
from sympy.core.sympify import sympify
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def series(expr, x=None, x0=0, n=6, dir="+"):
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"""Series expansion of expr around point `x = x0`.
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Parameters
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==========
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expr : Expression
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The expression whose series is to be expanded.
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x : Symbol
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It is the variable of the expression to be calculated.
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x0 : Value
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The value around which ``x`` is calculated. Can be any value
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from ``-oo`` to ``oo``.
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n : Value
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The number of terms upto which the series is to be expanded.
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dir : String, optional
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The series-expansion can be bi-directional. If ``dir="+"``,
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then (x->x0+). If ``dir="-", then (x->x0-). For infinite
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``x0`` (``oo`` or ``-oo``), the ``dir`` argument is determined
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from the direction of the infinity (i.e., ``dir="-"`` for
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``oo``).
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Examples
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========
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>>> from sympy import series, tan, oo
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>>> from sympy.abc import x
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>>> f = tan(x)
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>>> series(f, x, 2, 6, "+")
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tan(2) + (1 + tan(2)**2)*(x - 2) + (x - 2)**2*(tan(2)**3 + tan(2)) +
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(x - 2)**3*(1/3 + 4*tan(2)**2/3 + tan(2)**4) + (x - 2)**4*(tan(2)**5 +
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5*tan(2)**3/3 + 2*tan(2)/3) + (x - 2)**5*(2/15 + 17*tan(2)**2/15 +
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2*tan(2)**4 + tan(2)**6) + O((x - 2)**6, (x, 2))
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>>> series(f, x, 2, 3, "-")
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tan(2) + (2 - x)*(-tan(2)**2 - 1) + (2 - x)**2*(tan(2)**3 + tan(2))
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+ O((x - 2)**3, (x, 2))
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>>> series(f, x, 2, oo, "+")
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Traceback (most recent call last):
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...
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TypeError: 'Infinity' object cannot be interpreted as an integer
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Returns
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=======
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Expr
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Series expansion of the expression about x0
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See Also
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========
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sympy.core.expr.Expr.series: See the docstring of Expr.series() for complete details of this wrapper.
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"""
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expr = sympify(expr)
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return expr.series(x, x0, n, dir)
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