A Generalization of Heaviside's Expansion Theorem
W. O. Pennell · Bell System Technical Journal · 1929
The expansion theorem is one of the most frequently used methods of evaluating operational Forms arising from the operational calculus developed by Heaviside. The original theorem, however, is applicable, in general, only to expressions containing integral powers of the operator d/dt. This paper describes an extension to, or a generalization of the original expansion theorem whereby, in general, operational forms with either fractional or integral powers of the operator can be evaluated. A number of operational equivalents are given to be used with the theorem, one of which is the equivalent used by Heaviside. Examples of the application of the theorem to electric circuit problems are shown.