The concepts of Bernoulli numbers Bn, Bernoulli polynomials
Bn(x), and the generalized Bernoulli numbers Bn(a,b) are
generalized to the one Bn(x;a,b,c) which is called the
generalized Bernoulli polynomials depending on three positive
real parameters. Numerous properties of these polynomials and
some relationships between Bn, Bn(x), Bn(a,b), and
Bn(x;a,b,c) are established.