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Formal Power Series

A formal power series, sometimes simply called a "formal series" (Wilf 1994), of a field F is an infinite sequence {a_0,a_1,a_2,...} over F. Equivalently, it is a function from the set of nonnegative integers to F, {0,1,2,...}->F. A formal power series is often written

a_0+a_1x+a_2x^2+...+a_nx^n+...,

but with the understanding that no value is assigned to the symbol x.

See also

Generating Function, Power Series

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References

Henrici, P. "Definition and Algebraic Properties of Formal Series." §1.2 in Applied and Computational Complex Analysis, Vol. 1: Power Series-Integration-Conformal Mapping-Location of Zeros. New York: Wiley, pp. 9-13, 1988.Wilf, H. Generatingfunctionology, 2nd ed. New York: Academic Press, 1994.

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Formal Power Series

Cite this as:

Weisstein, Eric W. "Formal Power Series." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FormalPowerSeries.html

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