A generalization of the Sα-summation method

Abstract

In 1949, Meyer-König (5) introduced the so-called Sα-method of summability which is one of a family of transformations including the Euler, Borel and Taylor methods. Later in 1959, Jakimowski (3) defined the [F, dn] transformation which includes the Euler method as a special case. If {dn} is given infinite sequence and E denotes the displacement operator (i.e. Eks0 = sk), then the [F, dn] transformation of {sn} is given by {tn} where