(p; q)-FIBONACCI AND (p; q)-LUCAS SUMS BY THE DERIVATIVES OF SOME POLYNOMIALS

Abstract

The main purpose of this paper is to survey several sum formulae of (p,q)-Fibonacci number U_{n} and (p,q)-Lucas number V_{n} by using the first and the second derivatives of the equations

xⁿ=(x²-px+q)(∑U_{j}x^{n-1-j})+U_{n}x-qU_{n-1}

and

2xⁿ⁺¹-pxⁿ=(x²-px+q)(∑V_{j}x^{n-1-j})+V_{n}x-qV_{n-1}.

Keywords

• Fibonacci polynomial
• Lucas polynomial
• sum of products

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