A Continuous Analogue of Lattice Path Enumeration: Part II

Here are exhibited some additional results about the continuous binomial coefficients as introduced by L. Cano and R. Diaz in [1].Comment: second versio

General Convolution Identities for Bernoulli and Euler Polynomials

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 \ge 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.Comment: 20 page