FindGeneratingFunction

FindGeneratingFunction[{a1, a2, ...}, x]
attempts to find a simple generating function in x whose n^(th) series coefficient is .

FindGeneratingFunction[{{n1, a1}, {n2, a2}, ...}, x]
attempts to find a simple generating function whose ^(th) series coefficient is .

Details and OptionsDetails 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:
  • 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.
  • FindGeneratingFunction[list, x] only returns functions that correctly reproduce all elements of list.
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