On the Laplace transforms of retarded, Lorentz-invariant functions

A note on the comparison between Laplace and Sumudu transforms

Nonsmooth Analysis of Lorentz Invariant Functions

A real valued function g(x, t) on Rn×R is called Lorentz invariant if g(x, t) = g(Ux, t) for all n×n orthogonal matrices U and all (x, t) in the domain of g. In other words, g is invariant under the linear orthogonal transformations preserving the Lorentz cone: {(x, t) ∈ Rn × R | t ≥ ‖x‖}. It is easy to see that every Lorentz invariant function can be decomposed as g = f ◦ β, where f : R2 → R i...

The h-Laplace and q-Laplace transforms

Article history: Received 12 May 2009 Available online 6 October 2009 Submitted by B.S. Thomson

On Laplace Transforms Near the Origin

Let /(f) be locally integrable on [0, °°) and let L{f}(s) denote the Laplace transform of /(f). In this note, we prove that if/(f) ~ f Sh=q an(log f)~ as f -> °°, where 0 < Re ß < 1, then /.{/}($) ~ s^1 2^=0 cn('°8 '/*)"" as s ->• 0 in larg si « 7r/2 A, the cn being constants.

New Laplace transforms of Kummer's confluent hypergeometric functions

In this paper we aim to show how one can obtain so far unknown Laplace transforms of three rather general cases of Kummer’s confluent hypergeometric function 1F1(a; b; x) by employing generalizations of Gauss’s second summation theorem, Bailey’s summation theorem and Kummer’s summation theorem obtained earlier by Lavoie, Grondin and Rathie. The results established may be useful in theoretical p...