Applications of an identity of Bat{\i}r

TL;DR

This paper explores new mathematical identities derived from Bat{
31}r's identity, focusing on double sums involving well-known number sequences and binomial transforms, expanding the theoretical understanding of these mathematical structures.

Contribution

It introduces novel identities for double sums related to number sequences and binomial transforms based on Bat{
31}r's identity, enriching the field of mathematical identities.

Findings

Derived new identities for double sums involving number sequences.

Proved identities for binomial transform pairs.

Extended the theoretical framework of Bat{
31}r's identity.

Abstract

Based on an interesting identity of Bat{\i}r we derive new identities for double sums involving famous number sequences. We also prove some double sum identities for binomial transform pairs.