Incomplete Bivariate Fibonacci and Lucas p-Polynomials

الملخص EN

We define the incomplete bivariate Fibonacci and Lucas p-polynomials.

In the case x=1, y=1, we obtain the incomplete Fibonacci and Lucas p-numbers.

If x=2, y=1, we have the incomplete Pell and Pell-Lucas p-numbers.

On choosing x=1, y=2, we get the incomplete generalized Jacobsthal number and besides for p=1 the incomplete generalized Jacobsthal-Lucas numbers.

In the case x=1, y=1, p=1, we have the incomplete Fibonacci and Lucas numbers.

If x=1, y=1, p=1, k=⌊(n-1)/(p+1)⌋, we obtain the Fibonacci and Lucas numbers.

Also generating function and properties of the incomplete bivariate Fibonacci and Lucas p-polynomials are given.