On a polynomial sequence associated with the Bessel operator
Résumé
By means of the Bessel operator a polynomial sequence is constructed to which several properties are given. Among them are its explicit expression, the connection with the Euler numbers, and its integral representation via the Kontorovich-Lebedev transform. Despite its non-orthogonality (with respect to an $ L_{2}$-inner product), it is possible to associate to the canonical element of its dual sequence a positive-definite measure as long as certain stronger constraints are imposed.