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General convolutions identities for Bernoulli and Euler polynomials

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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Submitted on : Friday, April 10, 2020 - 2:54:13 PM
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Karl Ditcher, Christophe Vignat. General convolutions identities for Bernoulli and Euler polynomials. 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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