Abstract
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.