On $(p,q)-$Fibonacci Polynomials Connected with Finite Operators

Abstract

The aim of this study is to obtain some properties of the $(p,q)-$Fibonacci finite operator polynomials by implementing the finite operator to the $(p,q)-$ Fibonacci polynomials. Firstly, we obtain the Binet formula, generating function, exponential generating function, Poisson generating function, and binomial sum of $(p,q) -$ Fibonacci finite operator polynomials. After that we give determinantal expressions for these finite operator polynomials and their special cases. Lastly, we regain, in a different way, recurrence relation for these finite operator polynomials.

Keywords

• Binet-like formula
• generating function
• finite operator
• tridiagonal determinant.
• (p,q)-Fibonacci polynomials

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