General convolution identities for Bernoulli and Euler polynomials

作者：Dilcher Karl^*; Vignat Christophe

来源：Journal of Mathematical Analysis and Applications, 2016, 435(2): 1478-1498.

DOI：10.1016/j.jmaa.2015.11.006

• Bernoulli polynomials
• Euler polynomials
• Bernoulli numbers
• Euler numbers
• Convolution identities

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 Mild and Matiyasevich for Bernoulli numbers are special cases of the same general formula.

• 出版日期2016-3-15