In this paper, we introduce \(h(\xi )\) -Fibonacci-Lucas polynomials, k-Fibonacci-Hermite numbers, \(h(\xi )\) -Fibonacci-Hermite polynomials, Lucas-Hermite numbers and \(h(\xi )\) -Lucas-Hermite polynomials, where \(h(\xi )\) is a polynomial with real coefficients. The resulting formulas allow a considerable unification because the given definition uncovers and brings into focus patterns and properties shared by different classes of special functions and number theory. We obtain new representations, sums and identities which arise from various forms of generating functions.
