On the representation of $\langle\rho_j, W_j\rangle$ absolute monotone functions

In the paper [1] the notion of the $\langle\rho_j, W_j\rangle$ absolutely monotone function was introduced. In the present paper we give some examples of sequences $\Big\{W_j (x)\Big\}^{\infty}_0$ consider the corresponding classes of $\langle\rho_j, W_j\rangle$ absolute monotone functions and study the problems of thei representation.