In this paper, we introduce Mersenne and Mersenne-Lucas hybrinomial quaternions present some of their properties. Some identities are derived for these polynomials. Furthermore, give the Binet formulas, Catalan, Cassini, d’Ocagne identity generating exponential function quaternions.

Abstract.In this paper, the generalized Bessel matrix polynomials are introduced, starting from the hypergeometric matrix function. Integral form, Rodrigues’s formula and generating matrix function are then developed for the generalized Bessel matrix polynomials. These polynomials appear as finite series solutions of second-order matrix differential equations and orthogonality property for the ...

where a, b and (yn)n>o take values in some specified ring and a and b are fixed elements which do not depend on the Integer index n. A solution (yn)„^0 ^ completely specified once the values of yQ and yx are given. It is customary to denote by Fn(a, b) the solution corresponding to the choice y0 = 0, yt = l, and by Ln(a, b) the solution corresponding to the choice y0 = 2, yx = a. Loosely speaki...

Some new formulas related to the well-known symmetric Lucas polynomials are primary focus of this article. Different approaches used for establishing these formulas. A matrix approach is followed in order obtain some fundamental properties. Particularly, recurrence relations and determinant forms determined by suitable Hessenberg matrices. Conjugate generating functions derived examined. Severa...

We study the previously introduced bracketed tiling construction and obtain direct proofs of some identities for the Fibonacci and Lucas numbers. By adding a new type of tile we call a superdomino to this construction, we obtain combinatorial proofs of some formulas for the Fibonacci and Lucas polynomials, which we were unable to find in the literature. Special cases of these formulas occur in ...

We continue our study on relationships between Fibonacci (Lucas) numbers and Bernoulli polynomials. The derivations of results are based functional equations for the respective generating functions, which in case combinations hyperbolic functions. Special cases some corollaries will highlight interesting aspects findings.

We investigate the Fibonacci pseudoprimes of level k, and we disprove a statement concerning relationship between sets different levels, also discuss counterpart this result for Lucas k. then use some recent arithmetic properties generalized Lucas, Pell–Lucas sequences, to define new types levels k+ k− parameter a. For these novel pseudoprime sequences basic calculate numerous associated intege...