This is documentation for Mathematica 7, which was
based on an earlier version of the Wolfram Language.

# FindGeneratingFunction

 FindGeneratingFunction[{a1, a2, ...}, x] attempts to find a simple generating function in x whose n series coefficient is an. FindGeneratingFunction[{{n1, a1}, {n2, a2}, ...}, x]attempts to find a simple generating function whose ni 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.
 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.
Find a generating function for a sequence:
A periodic sequence:
Find a generating function for a sequence:
 Out[1]=
 Out[2]=

A periodic sequence:
 Out[1]=
 Out[2]=
 Scope   (2)
Rational functions:
Hypergeometric functions:
FindGeneratingFunction works on arbitrary exact numbers or symbolic expressions:
Use FindSequenceFunction to find a generating function of a sequence:
Verify:
New in 7