Hermite Polynomials and their Applications Associated with Bernoulli and Euler Numbers - Dae San Kim; Taekyun Kim; Seog-Hoon Rim; Sang Hun Lee (Discrete Dynamics in Nature and Society)
We derive some interesting identities and arithmetic properties of Bernoulli and Euler polynomials from the orthogonality of Hermite polynomials. Let Pn={p(x)∈ℚ[x]∣deg p(x)≤n} be the (n+1)-dimensional vector space over ℚ. Then we show that {H0(x),H1(x),…,Hn(x)} is a good basis for the space Pn for our purpose of arithmetical and combinatorial applications.