gfun[listtoratpoly] - find a rational generating function
gfun[seriestoratpoly] - find a rational approximation
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Calling Sequence
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listtoratpoly(l, x, [typelist])
seriestoratpoly(s, [typelist])
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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; variable name
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typelist
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(optional) list of generating function types. The default is 'ogf','egf'. For a complete list of types, see gftypes.
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s
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series
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Description
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The listtoratpoly(l, x, [typelist]) command computes a rational function in x for the generating function of the expressions in l. This generating function is one of the types specified by typelist, for example, ordinary (ogf) or exponential (egf). For a complete list of available generating function types, see gftypes.
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You should specify as many terms as possible in the list l.
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The seriestoratpoly(s, x, [typelist]) command computes a rational function in x for the generating function of the expressions in s. This generating function is one of the types specified by typelist, for example, ordinary (ogf) or exponential (egf). For a complete list of available generating function types, see gftypes.
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You should specify as many terms as possible in the series s.
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If typelist contains more than one element, these types are considered in the order that they are listed.
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If typelist is not specified, the default typelist, 'ogf','egf' is used.
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The function returns a list whose first element is the rational function. The second element is the generating function type for which a solution was found.
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These functions are frontends to convert[ratpoly] which performs the actual computation.
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Examples
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If the input is the first few elements of the Fibonacci sequence, the function returns the generating series for the Fibonacci numbers.
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