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Results tagged with generating-functions
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user 10881
A generating function is a way of encoding an infinite sequence of numbers by treating them as the coefficients of a formal power series. Tag questions involving generating functions in this.
9
votes
Accepted
Software for recognizing algebraic or D-finite formal power series
Fricas is good at that. It can be accessed via sage, once installed.
sage: L=[catalan_number(i) for i in range(20)]
sage: fricas.guessHolo(L) …
- 3,597
5
votes
Accepted
an algebra generated by some known series
This has been considered by Dimitri Zvonkine, see his article "An algebra of power series arising in the
intersection theory of moduli spaces of curves
and in the enumeration of ramified coverings
of …
- 3,597
4
votes
A continued J fraction for $a_n = \frac{1}{(n+1)^2}$?
Sagemath can do that too
sage: x = PowerSeriesRing(QQ,'x').gen()
sage: f = sum(x**n/(n+1)**2 for n in range(20)).O(20)
sage: f.jacobi_continued_fraction()
((-1/4, -7/144),
(-13/28, -647/110 …
- 3,597