Differentiably finite function

In mathematics, a differentiably finite function of one variable, also referred to as a D‑finite or holonomic function, is an analytic function which is a solution of a linear differential equation with polynomial coefficients. A differentiably finite (or D‑finite, or holonomic) power series is a formal power series that formally satisfies a linear differential equation with polynomial coefficients.

Formal definition

P-recursive sequences

Closure properties

In combinatorics

In computer algebra: differential equations as a data structure

Computation

Further reading

• Flajolet, Philippe; Sedgewick, Robert. Analytic Combinatorics. Cambridge University Press. ISBN 0521898064.
• Kauers, Manuel; Paule, Peter. The Concrete Tetrahedron. Text and Monographs in Symbolic Computation. Springer. ISBN 978-3-7091-0444-6.
• Stanley, Richard P. (1999). Enumerative Combinatorics, Volume 2. Cambridge University Press. ISBN 0-521-56069-1.