convert a list into a series
convert a series into a list
convert a list into a list
convert a series into a series
listtoseries(l, x, gf)
name; unknown variable
(optional) generating function type, e.g., 'egf' or 'ogf'
The listtoseries(l, x, gf) command accepts a list as input and returns a series.
By default, the listtoseries function creates a power series whose coefficients are exactly the elements of the list specified.
The listtolist(l, gf) command accepts a list as input and returns a list.
By default, the listtolist function returns the input list unchanged.
The seriestolist(s, gf) command accepts a series as input and returns a list.
By default, the seriestolist command returns a list whose entries are exactly the coefficients of the series specified.
The seriestoseries(s, gf) command accepts a series as input and returns a series.
By default, the seriestoseries function returns the input series unchanged.
Lists are viewed as lists of coefficients of power series and reciprocally series are viewed as generating series of lists of coefficients.
If gf is specified, it is considered to be a type of generating function. The coefficients of the output are those of the corresponding generating function of the input.
E.g., listtoseries(l, x, 'egf') resp. listtolist(l, 'egf') returns the series resp. the list whose coefficients are li+1i! for 0≤i. Similarly, if s is a series with coefficients si for 0≤i, then seriestoseries(s, 'egf') resp. seriestolist(s, 'egf') returns the series resp. the list whose coefficients are sii!.
l ≔ 1,1,2,5,14,42,132,429,1430,4862,16796,58786:
The LambertW function is the inverse of y⁢ⅇ−y. The following is a simple way to compute Taylor expansions of such functions.
S ≔ series⁡y⁢ⅇ−y,y
You can then extract the list of coefficients.
L ≔ seriestolist⁡
Multiplying the nth coefficient by n! recovers the number of planar trees of size n.
Download Help Document