Generalizations of Bernoulli numbers and polynomials

Abstract

The concepts of Bernoulli numbersBn, Bernoulli polynomialsBn(x), and the generalized Bernoulli numbersBn(a,b)are generalized to the oneBn(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 betweenBn,Bn(x),Bn(a,b), andBn(x;a,b,c)are established.