Analysis of multiindices and multivariable Voigt function via polynomials and numbers

The Voigt functions which appear frequently in the problems of astrophysical spectroscopy and neutron physics are extended and investigated. Various expansions and unified representations are derived related to lately introduced $k$-Fibonacci-Hermite numbers, $h(\rho)$-Fibonacci-Hermite polynomials, Lucas-Hermite numbers and $h(\rho)$-Lucas-Hermite polynomials $h(\rho)$ being a polynomial with real coefficients. The generalization of Voigt function provide interesting relationships with different polynomial families and allow a substantial unification of results in literature.