Generating Functions of Even and Odd Gaussian Numbers and Polynomials

In the present article, we introduce two new notions, which are called Gaussian ( p, q)-Jacobsthal numbers sequence [Formula: see text] and Gaussian ( p, q)-Jacobsthal Lucas numbers sequence [Formula: see text], and we present and prove our exciting properties and results, which relate these sequences. We first give recurrence relations, Binet’s formulas, explicit formulas, and negative extensions of them. We then obtain some important identities for Gaussian ( p, q)-Jacobsthal and Gaussian ( p, q)-Jacobsthal Lucas numbers and some connection formulas between these Gaussian numbers. After that, we give some summation formulas and the symmetric functions of Gaussian ( p, q)-Jacobsthal and Gaussian ( p, q)-Jacobsthal Lucas numbers. In addition, by using the symmetric functions, we derive a new class of generating functions for Gaussian ( p, q)-Jacobsthal and Gaussian ( p, q)-Jacobsthal Lucas numbers.

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Gaussian (p, q)-Jacobsthal and Gaussian (p, q)-Jacobsthal Lucas numbers and their some interesting properties

Saba

Boussayoud

2022

Journal of Mathematical Physics

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Generating functions of binary products of (p,q)-Fibonacci-like numbers with odd and even certain numbers and polynomials

Saba

Boussayoud

2022

Filomat

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In this paper, we study the symmetric and the generating functions for odd and even terms of the second-order linear recurrence sequences. we introduce a operator in order to derive a new family of generating functions of odd and even terms of Mersenne numbers, Mersenne Lucas numbers, (p,q)- Fibonacci-like numbers, k-Pell polynomials and k-Pell Lucas polynomials. By making use of the operator defined in this paper, we give some new generating functions of the products of (p,q)-Fibonacci-like numbers with odd and even terms of certain numbers and polynomials.

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Generating Functions of Even and Odd Gaussian Numbers and Polynomials

Cited by 2 publications

References 15 publications

Gaussian (p, q)-Jacobsthal and Gaussian (p, q)-Jacobsthal Lucas numbers and their some interesting properties

Gaussian (p, q)-Jacobsthal and Gaussian (p, q)-Jacobsthal Lucas numbers and their some interesting properties

Generating functions of binary products of (p,q)-Fibonacci-like numbers with odd and even certain numbers and polynomials

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