Pertemuan
6
Fungsi Gamma & Beta
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The (complete) gamma function
is defined to be an
extension of the factorial to complex and real number
arguments. It is related to the factorial by
. It is analytic everywhere except at z = 0, -1, -2, ..., and
the residue at
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is
2
Fungsi Gamma
Euler's gamma function is defined by the integral
Some further values of the Gamma function for small arguments are:
1,0
1,1
1,2
1,3
1,4
1,5
1,6
1,7
1,8
1,9
2,0
1,0000
0,9514
0,9182
0,9875
0,8873
0,8862
0,8935
0,9086
0,9314
0,9618
1,0000
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If x is an integer n = 1, 2, 3, ..., then
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Γ(n+1) = n Γ(n)
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Contoh

a.
3 -x
x
 e dx  ( 4 )  3!  3 x 2 x 1  6
.
0


3
 2x  2x
3 2x
x
e
dx

0
0  2  e d (2 x / 2)
b.
1
3
 (4) 
16
8
Contoh


x e 3
x
dx ,
misalkan
y 3 x
0
x = 1/9 y2

dx = 2/9 y dy
(3) 
4
27

2/27
2 y
y
.
 e dy 
0
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2/27
7
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The gamma function satisfies the functional
equations
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http://www.stat.vt.edu/~sundar/java/applets/Distributions.html#BETAFUNC
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http://www.stat.vt.edu/~sundar/java/applets/Distributions.html#GAMMAFUNC
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http://www.earlevel.com/Digital%20Audio/harmonigraf.html
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