ABSTRACT
The gamma function, denoted Γ(x), is defined by
Γ( ) , 0 0
x e t dt xt x= >− − ∞ ∫ 1
Properties
Γ Γ
Γ
Γ Γ
( ) ( )
( )
( ) !
x x x x
n n n n n
+ = >
=
+ = = =
1 0
1 1
1 1 2
,
( ) ( , ,
x x x
,…)
( ) /sin
(
Γ Γ
Γ
Γ
( ) − =
=
π π
π
) ( )Γ Γx x+
=1
2 2π
•
3. Laplace Transforms
The Laplace transform of the function f(t), denoted by F(s) or L{f(t)}, is defined
F s f t e dt st( ) =
provided that the integration may be validly performed. A sufficient condition for the existence of F(s) is that f(t) be of exponential order as t→∞ and that it is sectionally continuous over every finite interval in the range t ≥ 0. The Laplace transform of g(t) is denoted by L g t{ ( )} or G(s).
