Integrals of products of Bernoulli polynomials

Extending known results on integrals of products of two or three Bernoulli polynomials with limits of integration 0 and 1, we obtain identities for such integrals with limits of integration 0 and x, for a variable x. As applications we obtain certain quadratic and cubic identities for Bernoulli poly...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2011-09, Vol.381 (1), p.10-16
Main Authors: Agoh, Takashi, Dilcher, Karl
Format: Article
Language:English
Subjects:
Algebra
Bernoulli numbers
Bernoulli polynomials
Difference and functional equations, recurrence relations
Exact sciences and technology
Integrals
Mathematical analysis
Mathematics
Measure and integration
Number theory
Numerical analysis
Numerical analysis. Scientific computation
Recurrence relations
Sciences and techniques of general use
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Summary:Extending known results on integrals of products of two or three Bernoulli polynomials with limits of integration 0 and 1, we obtain identities for such integrals with limits of integration 0 and x, for a variable x. As applications we obtain certain quadratic and cubic identities for Bernoulli polynomials.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2011.03.061