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Generating Functions, Umbral Calculus, and Related Ideas

Topics in Generating Functions, Umbral Calculus, and Related Ideas

Numbered in the order to learn them.

  1. Motivation of "Formal" Power Series

  2. Generating Functions, and References

  3. Shift Operators

  4. Ordinary vs. Exponential Generating Functions

  5. Convolution of Sequences

  6. Fourier/Laplace Transform as Continuous Generating Function

  7. Fourier Series as Multiplicative Version of Generating Function

  8. Vandemonde's Identity

  9. Full Solution to Linear Recurrences

  10. Discrete Calculus in Terms of Generating Functions?

  11. Binomial-Type Identities

  12. Partitions and the Pentagonal Number Theorem

  13. Alternative Perspectives on Beta and Gamma Functions

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