Abstract By means of the telescoping method, several summation formulae are established for arctangent function with its argument being Pell and Pell–Lucas polynomials. Numerous infinite series identities involving Fibonacci Lucas numbers included as particular cases.

For an arbitrary homogeneous linear recurrence sequence of order d with constant coe cients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coe cients of these recurrences are given explicitly in terms of partial Bell polynomials that depend on at most d 1 terms of the generalized Lucas sequence associated with the given recurrence. We also provi...

We give a family of D5-polynomials with integer coefficients whose splitting fields over Q are unramified cyclic quintic extensions of quadratic fields. Our polynomials are constructed by using Fibonacci, Lucas numbers and units of certain cyclic quartic fields.

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

In this paper we consider the generalized order-k Fibonacci and Lucas numbers. We give the generalized Binet formula, combinatorial representation and some relations involving the generalized order-k Fibonacci and Lucas numbers.

Relation of hyperbolons of volume one to generalized Clifford algebras is described in [1b] and there some applications are listed. In this note which is an extension of [8] we use the one parameter subgroups of the group of hyperbolons of volume one in order to define and investigate generalization of Tchebysheff polynomial system. Parallely functions of roots of polynomials of any degree are ...

In this study we define and study the Bivariate Complex Fibonacci and Bivariate Complex Lucas Polynomials. We give generating function, Binet formula, explicit formula and partial derivation of these polynomials. By defining these bivariate polynomials for special cases Fn(x, 1) is the complex Fibonacci polynomials and Fn(1, 1) is the complex Fibonacci numbers. Finally in the last section we gi...

In geometric function theory, Lucas polynomials and other special have recently gained importance. this study, we develop a new family of bi-univalent functions. Also examined coefficient inequalities Fekete-Szegö problem for via these polynomials.