Abstract
In this paper, we derive the identities of higher-order Bernoulli, Euler and Frobenius-Euler polynomials from the orthogonality of Hermite polynomials. Finally, we give some interesting and new identities of several special polynomials arising from umbral calculus. MSC: 05A10, 05A19.
Highlights
The Hermite polynomials are defined by the generating function to be e xt–t = eH(x)t = ∞ tn Hn(x) n! n= ( . )with the usual convention about replacing Hn(x) by Hn(x)
1 Introduction The Hermite polynomials are defined by the generating function to be e xt–t = eH(x)t =
We introduce the identities of several special polynomials which are derived from the orthogonality of Hermite polynomials
Summary
1 Introduction The Hermite polynomials are defined by the generating function to be e xt–t = eH(x)t = X = , Hn( ) = Hn are called the nth Hermite numbers. The Bernoulli polynomials of order r are defined by the generating function to be t et –
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