## Experimental Mathematics

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

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

François Bergeron and Simon Plouffe

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 25 March 2003

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1048610118

**Mathematical Reviews number (MathSciNet)**

MR1257287

**Zentralblatt MATH identifier**

0782.05004

**Subjects**

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

#### Citation

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