Généralisation d'identités de Carlitz,Howard et Lehmer

Divided differences provide an efficient method for computing with functions of several variables.In this note, we use them to generalize the Newton interpolation formula, and obtain an orthogonality relation (3.3). From this, we deduce two inversion formulas (3.4) and (3.8) involving two infinite sets of variables.The generating functions (1.1) to (1.4) of Carlitz and Howard are obtained by a mere specialization of variables in the preceding inversion formulas.As an illustration, we show how to recover several identities due to Carlitz and Lehmer, and we give a newq-analog of the generating series of the Howard numbers (formulas 4.22 and 4.23).