Product of two power series as a single power series

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Given two power series f(x) and g(x), how can we write their product as a single power series? Equivalently, what is the coefficient of each power of x in f(x)g(x)?

About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university.

#education #powerseries #maclaurinseries #summation #coefficients #polynomials #maths #mathematics #math
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