I am exploring options for using computer to extract the coefficient of $x^n$ from the Taylor series expansion of a function of $x$, where $n$ is kept as a symbolic entity. While Mathematica offers a function called SeriesCoefficient that achieves this, I am in search of an open source alternative that offers similar functionality. I looked into SageMath and SymPy. They do not seem to have this function. If you fix $n$ as a number, these two can get you the coefficient of $x^n$, but not when you keep $n$ as a symbol. Does anyone know of any open source software package that can perform this task?
2026-03-26 17:11:51.1774545111
Is There an Open Source Equivalent for Mathematica's SeriesCoefficient Function?
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Maxima can do this, and in particular this functionality can be accessed in SageMath using the Maxima subsystem as described briefly here: if
fis an expression involvingx, thenmaxima(f).powerseries(x,0)._sage_()will produce a symbolic form of the Taylor series expansion around $0$.