gfun[listtoseries] - convert a list into a series
gfun[seriestolist] - convert a series into a list
gfun[listtolist] - convert a list into a list
gfun[seriestoseries] - convert a series into a series
Calling Sequence
listtoseries(l, x, gf)
listtolist(l, gf)
seriestolist(s, gf)
seriestoseries(s, gf)
Parameters
l - a list
s - a series
x - the unknown variable
[gf] - (optional)
Description
- These procedures take as input a list or a series and yield a list or a series, according to their name.
- Lists are viewed as lists of coefficients of power series and reciprocally series are viewed are generating series of lists of coefficients.
By default, listtoseries creates a power series whose coefficients are the elements of the list given as argument. Similarly, seriestolist returns a list of the coefficients of the series given as argument. The other two procedures, listtolist and seriestoseries, default to identity.
- When a third argument is given, it is treated as a type of generating function. The coefficients of the output are those of the corresponding generating function of the coefficients of the input.
Examples
> with(gfun):
l:=[1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786]:
listtoseries(l,x,'egf');\[1+x +x^{2}+\frac{5}{6} x^{3}+\frac{7}{12} x^{4}+\frac{7}{20} x^{5}+\frac{11}{60} x^{6}+\frac{143}{1680} x^{7}+\frac{143}{4032} x^{8}+\frac{2431}{181440} x^{9}+\frac{4199}{907200} x^{10}+\frac{4199}{2851200} x^{11}+\mathrm{O}\! \left(x^{12}\right)\]