The Journal of the Australian Mathematical Society. Series B. Applied Mathematics

Research Article

Summing series arising from integro-differential-difference equations

P. Ceronea1 and A. Sofoa1

a1 Department of Computer and Mathematical Sciences, Victoria University of Technology, PO Box 14428, Melbourne City MC, VIC 8001, Australia.


By applying Laplace transform theory to solve first-order homogeneous differential-difference equations it is conjectured that a resulting infinite sum of a series may be expressed in closed form. The technique used in obtaining a series in closed form is then applied to other examples in teletraffic theory and renewal processes.

(Received April 13 1995)