Connection problems via lowering operators

摘要

The lowering operator σ associated with a polynomial set {Pn}n⩾0 is an operator not depending on n and satisfying the relation σ(Pn)=nPn-1. In this paper, we express explicitly the connection coefficients between two polynomial sets using their corresponding lowering operators. We obtain some well-known results as particular cases including some duplication and addition formulas.