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Nonlinear Identities for Bernoulli and Euler Polynomials

Date

2018

Authors

Dilcher, Karl

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Abstract

It is shown that a certain nonlinear expression for Bernoulli polynomials, related to higher-order convolutions, can be evaluated as a product of simple linear polynomials with integer coefficients. The proof involves higher-order Bernoulli polynomials. A similar result for Euler polynomials is also obtained, and identities for Bernoulli and Euler numbers follow as special cases.

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