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FindGeneratingFunction

FindGeneratingFunction[{a1, a2, ...}, x]
attempts to find a simple generating function in x whose n^(th) series coefficient is an.
FindGeneratingFunction[{{n1, a1}, {n2, a2}, ...}, x]
attempts to find a simple generating function whose ni^(th) series coefficient is ai.
  • The sequence elements an can be either exact numbers or symbolic expressions.
  • If FindGeneratingFunction cannot find a simple generating function that yields the specified sequence, it returns unevaluated.
FunctionSpaceAutomaticwhere to look for candidate simple generating functions
MethodAutomaticmethod to use
TimeConstraint10how many seconds to search a particular function space or perform a transformation
ValidationLengthAutomaticsequence 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.
Find a generating function for a sequence:
A periodic sequence:
Rational functions:
Hypergeometric functions:
FindGeneratingFunction works on arbitrary exact numbers or symbolic expressions:
Use FindSequenceFunction to find a generating function of a sequence:
Verify:
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