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
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Calling Sequence
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listtoseries(l, x, gf)
listtolist(l, gf)
seriestolist(s, gf)
seriestoseries(s, gf)
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Parameters
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l
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list
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x
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name; unknown variable
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gf
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(optional) generating function type, e.g., 'egf' or 'ogf'
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s
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series
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Description
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The listtoseries(l, x, gf) command accepts a list as input and returns a series.
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By default, the listtoseries function creates a power series whose coefficients are exactly the elements of the list specified.
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The listtolist(l, gf) command accepts a list as input and returns a list.
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By default, the listtolist function returns the input list unchanged.
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The seriestolist(s, gf) command accepts a series as input and returns a list.
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By default, the seriestolist command returns a list whose entries are exactly the coefficients of the series specified.
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The seriestoseries(s, gf) command accepts a series as input and returns a series.
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By default, the seriestoseries function returns the input series unchanged.
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Lists are viewed as lists of coefficients of power series and reciprocally series are viewed as generating series of lists of coefficients.
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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.
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Examples
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The LambertW function is the inverse of . The following is a simple way to compute Taylor expansions of such functions.
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You can then extract the list of coefficients.
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Multiplying the nth coefficient by recovers the number of planar trees of size n.
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