A short table of generating functions and related formulas

TL;DR

This paper provides a comprehensive table of generating functions, related formulas, and references, serving as a useful resource for applications involving discrete Laplace transforms and z-transforms.

Contribution

It compiles and summarizes key generating functions and formulas, including Lagrange's expansion, with references to established mathematical handbooks.

Findings

Provides a useful reference table for generating functions

Includes formulas related to discrete Laplace and z-transforms

References classical mathematical formulas in Abramowitz and Stegun

Abstract

A table of sums useful for generating function applications (discrete Laplace transforms or z-transforms). Related definitions and formulas (including Lagrange's expansion), and reference to formulas in Abramowitz and Stegun, Handbook of Mathematical Functions, are given.