On the integral of the product of four and more Bernoulli polynomials

Su Hu; Daeyeoul Kim; Min Soo Kim

doi:10.1007/s11139-013-9506-y

On the integral of the product of four and more Bernoulli polynomials

Su Hu
, Daeyeoul Kim
, Min Soo Kim^*

^*Corresponding author for this work

Department of Mathematics

Korea Advanced Institute of Science and Technology
McGill University
National Institute for Mathematical Sciences
Kyungnam University

Research output: Contribution to journal › Journal article › peer-review

8 Scopus citations

Abstract

In 1958, L.J. Mordell provided a 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 results in this direction, including those by Nörlund, Mordell, Carlitz, Agoh, and Dilcher, are special cases of the formulas given in this paper.

Original language	English
Pages (from-to)	281-293
Number of pages	13
Journal	Ramanujan Journal
Volume	33
Issue number	2
DOIs	https://doi.org/10.1007/s11139-013-9506-y
State	Published - 2014.02

Keywords

Bernoulli numbers
Bernoulli polynomials
Integrals
Recurrence relations

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10.1007/s11139-013-9506-y

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title = "On the integral of the product of four and more Bernoulli polynomials",

abstract = "In 1958, L.J. Mordell provided a 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 results in this direction, including those by N{\"o}rlund, Mordell, Carlitz, Agoh, and Dilcher, are special cases of the formulas given in this paper.",

keywords = "Bernoulli numbers, Bernoulli polynomials, Integrals, Recurrence relations",

author = "Su Hu and Daeyeoul Kim and Kim, \{Min Soo\}",

year = "2014",

month = feb,

doi = "10.1007/s11139-013-9506-y",

language = "English",

volume = "33",

pages = "281--293",

journal = "Ramanujan Journal",

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T1 - On the integral of the product of four and more Bernoulli polynomials

AU - Hu, Su

AU - Kim, Daeyeoul

AU - Kim, Min Soo

PY - 2014/2

Y1 - 2014/2

N2 - In 1958, L.J. Mordell provided a 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 results in this direction, including those by Nörlund, Mordell, Carlitz, Agoh, and Dilcher, are special cases of the formulas given in this paper.

AB - In 1958, L.J. Mordell provided a 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 results in this direction, including those by Nörlund, Mordell, Carlitz, Agoh, and Dilcher, are special cases of the formulas given in this paper.

KW - Bernoulli numbers

KW - Bernoulli polynomials

KW - Integrals

KW - Recurrence relations

UR - https://www.scopus.com/pages/publications/84893957085

U2 - 10.1007/s11139-013-9506-y

DO - 10.1007/s11139-013-9506-y

M3 - Journal article

AN - SCOPUS:84893957085

SN - 1382-4090

VL - 33

SP - 281

EP - 293

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 2

ER -

On the integral of the product of four and more Bernoulli polynomials

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Keywords

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