gfun[listtorec] - find a recurrence for the elements
gfun[seriestorec] - find a recurrence for the coefficients of a series
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Calling Sequence
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listtorec(l, u(n), [typelist])
seriestorec(s, u(n), [typelist])
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Parameters
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l
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list
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u
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name; function name
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n
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name; variable of the function u
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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 listtorec(l, u(n), [typelist]) command computes a linear recurrence with polynomial coefficients satisfied by the expressions in l. A normalization is 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 seriestorec(s, u(n), [typelist]) command computes a linear recurrence with polynomial coefficients satisfied by the expressions in s. A normalization is 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 a set containing the recurrence and its initial conditions. The second element is the generating function type to which it corresponds.
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Examples
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