Association of variables inn-dimensional Laplace transform

Abstract

Let f(t ₁ t ₂, [tdot], t _n rpar; be the inverse Laplace transform ℒ₁ ⁻¹ F of F(s ₁ s ₂, [tdot], s _n ). Then there exists a function G(s) such that ℒ₁ ⁻¹ G(s) = f(t ₁, t ₂, [tdot], t _n )|t ₁ = t ₂,= [tdot] = t_n = t-Chen and Chiu (1973) proved three theorems for evaluating the associated transform G(s) for certain types of F(s ₁, s ₂, [tdot], s_n ). In this paper, we give additional theorems for evaluating G(s).