General convolutions identities for Bernoulli and Euler polynomials, Journal of Mathematical analysis and Applications

Abstract : Using general identities for difference operators, as well as a technique of symbolic computation and tools from probability theory, we derive very general kth order (k >2) convolution identities for Bernoulli and Euler polynomials. This is achieved by use of an elementary result on uniformly distributed random variables. These identities depend on k positive real parameters, and as special cases we obtain numerous known and new identities for these polynomials. In particular we show that the well-known identities of Miki and Matiyasevich for Bernoulli numbers are special cases of the same general formula.
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https://hal.archives-ouvertes.fr/hal-01248271
Contributor : Christophe Vignat <>
Submitted on : Thursday, December 24, 2015 - 1:09:45 PM
Last modification on : Tuesday, December 18, 2018 - 10:56:29 AM

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Karl Ditcher, Christophe Vignat. General convolutions identities for Bernoulli and Euler polynomials, Journal of Mathematical analysis and Applications. Journal of Mathematical Analysis and Applications, Elsevier, 2016, 435 (2), pp.1478-1498. ⟨10.1016/j.jmaa.2015.11.006 ⟩. ⟨hal-01248271⟩

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