Finite sums and generalized forms of Bernoulli polynomials

Abstract

We introduce new classes of Bernoulli polynomials, useful to evaluate partial sums of Hermite and Laguerre polynomials. We also comment on the possibility of extending the class of Bernoulli numbers itself, and indicate their importance in the derivation of partial sums involving generalized forms of Hermite and Laguerre polynomials.

Keywords

• monomiality
• polynomials
• laguerre
• hermite
• bernoulli
• partial sums