A Table of Generating Functions

TL;DR

This paper compiles a comprehensive collection of generating functions involving sums, integrals, and special functions, serving as a valuable reference for researchers working with generating functions and their applications.

Contribution

It provides a systematic compilation of generating functions with complex sums and integrals, including special functions, which was not previously available in a unified form.

Findings

Extensive list of generating functions involving sums and integrals

Inclusion of special functions in both summands and solutions

Facilitates further research and applications in combinatorics and analysis

Abstract

This is a compendium of generating functions involving single, double sums and definite integrals. These generating functions also involve special functions in both the summand function and closed form solution.