{title2=$A(z)=\sum_{n\geq0}a_nz^n$}
{wiki=Generating_function}

The ordinary generating function of a sequence $(a_n)_{n\geq0}$ is the <formal power series> $A(z)=\sum_{n\geq0}a_nz^n$. Algebraic identities for $A$ encode recurrences and counting constructions for the coefficients.


Ordinary generating function

{title2=$R[[T]]$}
{wiki}

The <formal power series ring> $R[[T]]$ consists of all expressions $\sum_{n\geq0}a_nT^n$ with $a_n\in R$. Addition is coefficientwise, while multiplication uses the <Cauchy product>; no analytic convergence is required.

= Formal power series ring
{synonym}


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 Incoming links: Formal power series