# Some Variations of Two Combinatorial Identities

## TL;DR

This paper introduces new variations of existing combinatorial identities, proves them using integral representations, and shows how some known identities are special cases of these new results.

## Contribution

It presents novel variations of two known combinatorial identities and demonstrates their proofs via integral representations, expanding the understanding of these identities.

## Key findings

- New variations of combinatorial identities are established.
- Some existing identities are shown as special cases of the new ones.
- The integral representation method is effectively used for proofs.

## Abstract

Given two combinatorial identities proved earlier, a new set of variations of these combinatorial identities is listed and proved with the integral representation method. Some identities from literature are shown to be special cases of these new identities.