Generating Functions, Umbral Calculus, and Related Ideas
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- Motivation of "Formal" Power Series
- Generating Functions, and References
- Shift Operators
- Ordinary vs. Exponential Generating Functions
- Convolution of Sequences
- Fourier/Laplace Transform as Continuous Generating Function
- Fourier Series as Multiplicative Version of Generating Function
- Vandemonde's Identity
- Full Solution to Linear Recurrences
- Discrete Calculus in Terms of Generating Functions?
- Binomial-Type Identities
- Partitions and the Pentagonal Number Theorem
- Alternative Perspectives on Beta and Gamma Functions