The Dattoli–Srivastava conjectures concerning generating functions involving the harmonic numbers

In a recent paper Dattoli and Srivastava [3], by resorting to umbral calculus, conjectured several generating functions involving harmonic numbers. In this sequel to their work our aim is to rigorously demonstrate the truth of the Dattoli–Srivastava conjectures by making use of simple analytical arguments. In addition, one of these conjectures is stated and proved in more general form.