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

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.