Representations of degenerate Hermite polynomials

The study on degenerate versions of some special numbers and polynomials, which began with Carlitz's pioneering work, has regained recent interests mathematicians. Motivated by this, we introduce Hermite polynomials as a version the ordinary polynomials. Recently, introduced was ?-umbral calculus where usual exponential function appearing in generating Sheffer sequence is replaced function. Then, among other things, using formula about expressing one ?-Sheffer polynomial terms another represent higher-order Bernoulli, Euler, Frobenius-Euler vice versa.