Abstract
Let ℙn be the space of polynomials of degree less than or equal to n. In this article, using the Bernoulli basis {B0(x), . . . , Bn(x)} for ℙn consisting of Bernoulli polynomials, we investigate some new and interesting identities and formulae for the product of two Bernoulli and Euler polynomials like Carlitz did.
Highlights
The Bernoulli and Euler polynomials are defined by means of et t − ext 1 = ∞tn Bn(x) n!, et 2 + tn En(x) n! . (1) n=0 n=0In the special case, x = 0, Bn(0) = Bn and En(0) = En are called the n-th Bernoulli and Euler numbers.From (1), we note that n Bn(x) =
1 Introduction The Bernoulli and Euler polynomials are defined by means of et t −
In this article, using the Bernoulli basis {B0(x), . . . , Bn(x)} for Pn consisting of Bernoulli polynomials, we investigate some new and interesting identities and formulae for the product of two Bernoulli and Euler polynomials like Carlitz did
Summary
Introduction The Bernoulli and Euler polynomials are defined by means of et t − In [3,4], we can find the following formula for a product of two Bernoulli polynomials: Bm(x)Bn(x) = Bernoulli identities arising from Bernoulli basis polynomials From (1), we note that ext = 1 t t(et − 1) et − 1 ext Proposition 1 The set of Bernoulli polynomials {B0(x), B1(x), .
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