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Generating Functions: The Basics A formal power series is an expression of the form A generating function is a power series formed from a sequence Important Power Series Identity (ID1): Methodology: 1) Define generating function from sequence 2) Multiply both sides of recurrence by and sum over all 3) Express both sides of identity in terms of and solve for 4) Expand as a power series Example 1: Fibonacci Sequence Finding the general term: Define . Then: . Define also Then: Therefore, we have that Here is a more practical application: Example 2: What is the generating function for a partition of integers? Solution: into a sum of even positive