The purpose of this paper is to give identities and relations including the Milne-Thomson polynomials, the Hermite polynomials, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the central factorial numbers, and the Cauchy numbers. By using fermionic and bosonic p-adic integrals, we derive some new relations and formulas related to these numbers and polynomials, and also the combinatorial sums.
Keywords: Array polynomials; Bernoulli numbers and polynomials; Cauchy numbers; Central factorial numbers; Euler numbers and polynomials; Functional equation; Generating function; Hermite polynomials; Milne–Thomson polynomials; Special functions; Stirling numbers; p-adic integral.