attempts to find a simple generating function in x whose n series coefficient is an.
attempts to find a simple generating function whose ni series coefficient is ai.
Details and Options
- The sequence elements an 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.
Examplesopen allclose all
Generalizations & Extensions (1)
FindGeneratingFunction works on arbitrary exact numbers or symbolic expressions:
Properties & Relations (1)
Use FindSequenceFunction to find a generating function of a sequence:
Wolfram Research (2008), FindGeneratingFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/FindGeneratingFunction.html.
Wolfram Language. 2008. "FindGeneratingFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FindGeneratingFunction.html.
Wolfram Language. (2008). FindGeneratingFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindGeneratingFunction.html