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BUILT-IN MATHEMATICA SYMBOL
FindGeneratingFunction
FindGeneratingFunction[{a1, a2, ...}, x]
attempts to find a simple generating function in x whose n
series coefficient is 
.
FindGeneratingFunction[{{n1, a1}, {n2, a2}, ...}, x]
attempts to find a simple generating function whose 
series coefficient is 
.
Details and Options
- The sequence elements
can be either exact numbers or symbolic expressions. - FindGeneratingFunction finds results in terms of a wide range of integer functions, as well as implicit solutions to difference equations represented by DifferenceRoot.
- If FindGeneratingFunction cannot find a simple generating function that yields the specified sequence, it returns unevaluated.
- FindGeneratingFunction has the following options:
-
FunctionSpace Automatic where to look for candidate simple generating functions Method Automatic method to use TimeConstraint 10 how many seconds to search a particular function space or perform a transformation ValidationLength Automatic sequence length used to validate a candidate generating function found - FindGeneratingFunction[list, x] by default uses earlier elements in list to find candidate simple generating functions, then validates the generating functions by looking at later elements.
- FindGeneratingFunction[list, x] only returns functions that correctly reproduce all elements of list.
New in 7
