Contents

Ars Combinatoria

  • Research article

Some Identities on the Euler Numbers Arising from Euler Basis Polynomials

T. Kim1, D.S. Kim2, D.V. Dolgy3, S.H. Rim4
1Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea,
2Department of Mathematics, Sogang University, Seoul 121-741, Republic of Korea,
3HANRIMWON, KWANGWOON UNIVERSITY, SEOUL 139-701, REPUBLIC OF KOREa,
4Department of Mathematics Education, Kyungpook National University, Daegu 702-701, Republic of Korea,
  • Published: 30/04/2013

Abstract

In this paper, we show that the set \(\{E_0(x), E_1(x), \ldots, E_n(x)\}\) of Euler polynomials is a basis for the space of polynomials of degree less than or equal to \(n\). From the properties of Euler basis polynomials, we derive some interesting identities on the product of two Bernoulli and Euler polynomials.

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Citation
T. Kim, D.S. Kim, D.V. Dolgy, S.H. Rim. Some Identities on the Euler Numbers Arising from Euler Basis Polynomials[J], Ars Combinatoria, Volume 109. 433-446. .