Reciprocal formulae for convolutions of Bernoulli and Euler polynomials

Abstract

By computing the bivariate exponential generating functions for the Ω-functions, we investigate the reciprocal sums concerning Bernoulli and Euler polynomials. Their convolutions with different weight factors lead to numerous strange identities on Bernoulli and Euler polynomials, such as Miki’s identity and the recent generalizations due to Pan and Sun (2006).

Keywords

• generating function
• binomial convolution
• bernoulli polynomial
• euler polynomial
• miki’s identity