Construction of hybrid form of \(\Delta _h\)-Appell polynomials

In this article, a hybrid form of \(\Delta _h\) ${\mathrm{\Delta }}_h$ -Appell polynomials, namely the \(\Delta _h\) ${\mathrm{\Delta }}_h$ -Frobenius-Euler-Appell polynomials is investigated. The generating function, recurrence relation, explicit representations and implicit formulas involving \(\Delta _h\) ${\mathrm{\Delta }}_h$ -Frobenius-Euler-Appell polynomials is obtained. The \(\Delta _h\) ${\mathrm{\Delta }}_h$ -Frobenius-Euler-Appell polynomials are framed within the context of quasi-monomial principle. The determinant form for these polynomials are explored. Further, certain examples are considered as the special cases of \(\Delta _h\) ${\mathrm{\Delta }}_h$ -Frobenius-Euler-Appell polynomials.