The Laplace transform of exp( et)

Michael A. B. Deakin
1996 The Journal of the Australian Mathematical Society Series B Applied Mathematics  
In an earlier paper [4] , the author showed how Laplace transforms might be assigned to a class of superexponential functions for which the usual defining integral diverges. The present paper considers the case of the function exp(e'). which arises in combinatorial contexts and whose Laplace transform may be assigned by means of an extension of techniques described in the previous paper. and discuss the Laplace transform of F(t). Deakin's [4] technique for assigning Laplace transforms to
more » ... ransforms to analytic but superexponential functions such as F(t) is to expand the function as a Taylor series, take
doi:10.1017/s0334270000010663 fatcat:qgk6mbgzcrajtlbqrhu44x4b5u