Convolution Identities on the ApostolHermite Base of Two Variables Polynomials
In this paper, we introduce a linear differential operator and investigate its fundamental properties. By means of this operator we derive convolution identities for ApostolHermite base two variables polynomials. These identities extend the Eulers identities for the sums of product for the two variables Hermite base ApostolBernoulli and ApostolEuler polynomials. Applying this differential operator to some specials functions, we obtain interesting identities and formulae involving the two variables Hermite base ApostolBernoulli and two variables Hermite base ApostolEuler polynomials arising from the \(\lambda \)-Stirling numbers and two variables HermiteKamp de Friet polynomials.
\(\lambda \)-stirling numbers convolution sums apostol\(-\)hermite polynomials hermite\(-\)kamp de friet