Talha Usman

A New Class of Laguerre-based Generalized Apostol Polynomials

Abstract In this paper, we introduce a unified family of Laguerre-based Apostol Bernoulli, Euler and Genocchi polynomials and derive some implicit summation formulae and general symmetry identities arising from different analytical means and applying generating functions. The result extend some known summations and identities of generalized Bernoulli, Euler and Genocchi numbers and polynomials.

Certain unified polynomials

ABSTRACT We aim to introduce certain unified polynomials which can be specialized to yield a number of known polynomials and numbers, for example, Pell polynomials and numbers, Fibonacci polynomials and numbers, and -Fibonacci polynomials. Then we investigate the unified polynomials to present certain interesting and potentially useful properties such as explicit expressions, some recurrence relations, a differential equation, and several generating functions. Further, among a number of polynomials and numbers which can be specialized from the unified polynomials, we choose the Pell polynomials to record their corresponding properties.