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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2016

General convolutions identities for Bernoulli and Euler polynomials

Karl Ditcher
  • Fonction : Auteur
Christophe Vignat

Résumé

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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Dates et versions

hal-01248271 , version 1 (10-04-2020)

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