논문
On the integral of the product of four and more Bernoulli polynomials
- 저자Su Hu, Daeyeoul Kim, and Min-Soo Kim
- 학술지Ramanujan J. 33
- 등재유형
- 게재일자(2014)
In 1958, L.J. Mordell provided the formula for the integral of the product of two Bernoulli polynomials, he also remarked: The integrals containing the product of more than two Bernoulli polynomials do not appear to lead to simple results.
In this paper, we provide explicit formulas for the integral of the product of $r$ Bernoulli polynomials, where $r$ is any positive integer.
Many authors’ results in this direction, including Norlund, Mordell,Carlitz, Agoh and Dilcher are special cases of the formulas given in this paper.
In 1958, L.J. Mordell provided the formula for the integral of the product of two Bernoulli polynomials, he also remarked: The integrals containing the product of more than two Bernoulli polynomials do not appear to lead to simple results.
In this paper, we provide explicit formulas for the integral of the product of $r$ Bernoulli polynomials, where $r$ is any positive integer.
Many authors’ results in this direction, including Norlund, Mordell,Carlitz, Agoh and Dilcher are special cases of the formulas given in this paper.
