Fungsi Gamma & Beta
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Transcript of Fungsi Gamma & Beta
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Fungsi Gamma & BetaMatematika Lanjut II
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Fungsi Gamma
Defnisi dan Fungsi
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Fungsi Gamma
A. Fungsi Gamma
1. Defnisi Fungsi Gamma
Secara umum ungsi gamma didefnisikan sebagai integral tak wajar denumum sebagai berikut.
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Fungsi Gamma
2. Siatsiat Fungsi Gamma
!erikut adala" siatsiat #ang dimiliki ungsi gamma$
a.
!ukti $
Dengan menggunakan integral %arsial& maka $
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Fungsi Gamma
b.
Siat ini da%at dibuktikan dengan cara #ang sama %ada siat 'a(& #aitu$
)
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Fungsi Gamma
c.
!ukti
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Contoh Soal
*entukan nilai dari
+awab
+adi&
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Contoh Soal
Misal&
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Fungsi BetaDefnisi dan Fungsi
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Fungsi Beta
1. Defnisi Fungsi !eta
Fungsi !eta sering disimb,lkan dengan -'&#(. !entuk umum ungsi beta adala"
dimana k,n/ergen untuk
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Fungsi Beta
2. Siat Fungsi !eta
Siat ungsi beta adala" simetris& #aitu$
!ukti
Dengan menggunakan trans,rmasi & maka di%er,le" $
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Fungsi Beta
0. ubungan Fungsi Gamma dan Fungsi !eta
ubungan ungsi gamma dan ungsi beta adala" ba"wa ungsi beta da%at din#atakungsi gamma. ersamaan#a adala" sebagai berikut $
3ntuk & #ang meru%akan s#arat agar k,n/ergen. ersamaan di atas da%at ditunjuktrans,rmasi k,rdat %,lar
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Fungsi Beta
4. !entuk Integral #ang da%at din#atakan dalam Gamma dan !eta
!erikut adala" integral s%esial #ang din#atakan dalam ungsi gamma dan ungsi beta $
a.
!ukti $
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Contoh Soal
*entukan nilai dari $
+awab$
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Contoh Soal
5