Symmetric and generating functions of generalized (p,q)-numbers

Abstract

In this paper, we first define new generalization for (p,q)-numbers. Considering these sequence, we give Binet's formulas and generating functions 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. After that, we give some new generating functions for product of (p,q)-numbers with bivariate complex Fibonacci and Lucas polynomials.

Keywords

• Symmetric functions
• Generating functions
• Generalized (p
• q)-numbers
• (p
• q)-Pell numbers