ABSTRACT
If f(t) belongs to a class A (meaning that it is a piecewise continuous function over 0 ≤ t < ∞ and is of some exponential order), its Laplace transform f ¯ ( p ) $ \bar{f}(p) $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429503580/e8c17e8d-aa2b-4352-a3e7-8cf96212c2f8/content/inline-math4_1.tif"/> exists. This is denoted symbolically by L [ f ( t ) ; t → p ] = ∫ 0 ∞ e - p t f ( t ) d t ≡ f ¯ ( p ) $$ L[f(t);\,\,t \to p] = \mathop \smallint \limits_{0}^{\infty } e^{{ - pt}} f(t)dt \equiv \bar{f}(p) $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429503580/e8c17e8d-aa2b-4352-a3e7-8cf96212c2f8/content/math4_1.tif"/>
