In this paper we consider the generalized Jacobsthal Jn,m and Jacobsthal-Lucas numbers jn,m. Also, introduce new sequences of An,m, Bn,m, Cn,m Dn,m. Namely, these are convolutions Further, find generating functions some recurrence relations for numbers.

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

We define a new generalization of Gaussian Pell-Lucas polynomials. call it $d-$Gaussian Then we present the generating function and Binet formula for give matrix representation Using Riordan method, obtain factorizations Pascal involving

In this paper, we define and investigate modified p-Leonardo, p-Leonardo-Lucas p-Leonardo sequences as special cases of the generalized Leonardo sequence. We present Binet's formulas, generating functions, Simson summation formulas for these sequences. Moreover, give some identities matrices related with Furthermore, show that there are close relations between p-Leonardo-Lucas, numbers Fibonacc...

The Gauss-Lucas Theorem on the roots of polynomials nicely simplifies the computation of the subderivative and regular subdifferential of the abscissa mapping on polynomials (the maximum of the real parts of the roots). This paper extends this approach to more general functions of the roots. By combining the Gauss-Lucas methodology with an analysis of the splitting behavior of the roots, we obt...

Recently, Tremblay, Gaboury and Fugère introduced a class of the generalized Bernoulli polynomials (see Tremblay in Appl. Math. Let. 24:1888-1893, 2011). In this paper, we introduce and investigate an extension of the generalized Apostol-Euler polynomials. We state some properties for these polynomials and obtain some relationships between the polynomials and Apostol-Bernoulli polynomials, Stir...

Generalized polynomials are functions obtained from conventional polynomials by applying the operations of taking the integer part, addition, and multiplication. We construct a system of “basic” generalized polynomials with the property that any bounded generalized polynomial is representable as a piecewise polynomial function of these basic ones. Such a representation is unique up to a functio...