Some results due to Konhauser polynomials of first kind and Laguerre polynomials

摘要

The principal aim of this paper is to introduce new set of polynomialLmq(α,β)(z)=Γ(αm+β+1)m!∑n=0mq(-m)qnΓ(αn+β+1)znn!,whereα,β∈C;m,q∈N,mq denotes integral part of mq,Re(β)>-1. This new set of polynomials is generalization of the Konhauser polynomials and generalized Laguerre polynomials. For the polynomials Lmq(α,β)(z), its various properties including relation with generalized Mittag–Leffler function, integral representations, generalized hypergeometric series representations, finite summation formulae, generating relations, fractional integral operators and differentials operators, recurrence relations, integral transforms with their several interesting cases have been discussed.