ABSTRACT

The Nörlund principal sum will be further developed. The Nörlund form of the EulerMaclaurin expansion (3.70) will be rederived in a rigorous fashion and trigonometric developments for the sum will also be obtained. A special class of linear transformations will be studied whose domain is the class of entire functions of exponential type. Application of these transformations to the solution of certain functional equations will be made.