Construction of partially degenerate Laguerre–Bernoulli polynomials of the first kind

Abstract

In this paper, we introduce partially degenerate Laguerre–Bernoulli polynomials of the first kind and deduce some relevant properties by using a preliminary study of these polynomials. We derive some theorems on implicit summation formulae for partially degenerate Laguerre–Bernoulli polynomials of the first kind $ {}_LB_{j}(\xi,\eta |\lambda ) $ . Finally, we derive some symmetry identities for partially degenerate Laguerre–Bernoulli polynomials of the first kind.

Keywords

• laguerre polynomials
• partially degenerate bernoulli polynomials of the first kind
• partially degenerate laguerre–bernoulli polynomials of the first kind
• summation formulas
• symmetry identities