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The 45 pages that link to Generating function, each with the reason it gives.

• Circle methodNarrower topic: The method extracts and estimates coefficients from these power series.

• Hardy–Littlewood circle methodNarrower topic: The method packages candidate summands into a function whose powers encode additive representations.

• Jacobi triple productNarrower topic: The series expansion translates product factors into combinatorial counting data.

• q-seriesNarrower topic: A q-series is often used as a generating function whose variable tracks size or weight.

• Vandermonde's identityNarrower topic: Binomial expansions act as generating functions for the coefficients being convolved.

• Lagrange inversion theoremNarrower topic: Inversion is especially useful when a generating function is specified implicitly.

• Rogers–Ramanujan identitiesNarrower topic: The series sides use coefficients to record counts of restricted partitions.

• Pentagonal number theoremNarrower topic: The theorem transforms a product into a generating series with sparse coefficients.

• History of combinatoricsNarrower topic: Generating functions gave combinatorialists a systematic way to solve and combine counting problems.

• Hosoya indexNarrower topic: The matching polynomial packages matching counts by size, with the Hosoya index obtained by summing coefficients.