Abstract
Author presents a new family of generalized Voigt functions related to recently introduced k-Fibonacci–Hermite numbers, h(x)-Fibonacci–Hermite polynomials, Lucas–Hermite numbers and h(x)-Lucas–Hermite polynomials where h(x) is a polynomial with real coefficients. The multivariable extensions of these results provide a natural generalization and unification of integral representations which may be viewed as a new relationship for the product of two different families of Lucas and Hermite polynomials. Some interesting explicit series representations, integrals and identities are obtained. The resulting formulas allow a considerable unification of various special results which appear in the literature.
Published Version
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