Connection problems via lowering operators

The lowering operator σ associated with a polynomial set { P n } n ⩾ 0 is an operator not depending on n and satisfying the relation σ ( P n ) = nP n - 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.