Experimental Mathematics

Computing the generating function of a series given its first few terms

François Bergeron and Simon Plouffe


We outline an approach for the computation of a good candidate for the generating function of a power series for which only the first few coefficients are known. More precisely, if the derivative, the logarithmic derivative, the reversion, or another transformation of a given power series (even with polynomial coefficients) appears to admit a rational generating function, we compute the generating function of the original series by applying the inverse of those transformations to the rational generating function found.

Article information

Experiment. Math., Volume 1, Issue 4 (1992), 307-312.

First available in Project Euclid: 25 March 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]
Secondary: 11B65: Binomial coefficients; factorials; $q$-identities [See also 05A10, 05A30] 11Y16: Algorithms; complexity [See also 68Q25] 68Q40


Bergeron, François; Plouffe, Simon. Computing the generating function of a series given its first few terms. Experiment. Math. 1 (1992), no. 4, 307--312. https://projecteuclid.org/euclid.em/1048610118

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