On strongly reversible elements in the Riordan group

An element of a group is called reversible if it is conjugate to its inverse, and strongly reversible if it can be expressed as a product of two involutions. We study strongly reversible elements in the Riordan group and its various important subgroups. We prove that not every reversible element in the Riordan group is strongly reversible, and we investigate products of reversible elements in the Riordan group.