What type of study is this?

September 10, 2025Open Access

A new family of symmetric and generating functions of binary products of (p,q)-numbers at consecutive and nonconsecutive terms

NSNabiha SabaUniversity of Jijel ABAli BoussayoudUniversity of Jijel SBSalah BoulaarasQassim University

Key Points

New generating functions for (p,q)-numbers were established using a symmetrizing operator, enhancing existing knowledge.
The research reveals a new class of functions for products of various (p,q)-numbers, including their interactions with Mersenne numbers.
This application is significant for both consecutive and nonconsecutive terms within the sequence of these numbers.
The findings offer potential implications for further mathematical theories and applications related to number sequences.

Abstract

In this study, by making use of the symmetrizing operator ?k+1a1a2 we introduce a new theorem. By using this theorem we give a new class of generating functions of the products of (p, q)-Fibonacci numbers, (p, q)-Lucas numbers, (p, q)-Pell numbers, (p, q)-Pell Lucas numbers, (p, q)-Jacobsthal numbers and (p, q) -Jacobsthal Lucas numbers at consecutive and nonconsecutive terms and the products of these (p, q)-numbers with Mersenne numbers at consecutive and nonconsecutive terms.

AI से पूछें

Bookmark

View Full Paper