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Dina matematik, fungsi béta, mimitina disebut ogé integral Euler, nyaéta hiji fungsi husus nu dihartikeun ku
![{\displaystyle \mathrm {B} (x,y)=\int _{0}^{1}t^{x-1}(1-t)^{y-1}\,dt}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f4ab12be9722687a96ea0aa6ee3a3e45969053c9)
Fungsi béta nyaéta simétrik, hartina
![{\displaystyle \mathrm {B} (x,y)=\mathrm {B} (y,x).}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fb6b92ee28e56966202dc0ec1e07135007489024)
mibanda bentuk séjén, kaasup:
![{\displaystyle \mathrm {B} (x,y)={\frac {\Gamma (x)\Gamma (y)}{\Gamma (x+y)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/40b51751e249b6100af540a95d503198913c05e0)
![{\displaystyle \mathrm {B} (x,y)=2\int _{0}^{\pi /2}\sin ^{2x-1}\theta \cos ^{2y-1}\theta \,d\theta ,\qquad {\mathrm {R} e}(x)>0,\ {\mathrm {R} e}(y)>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2eabc0c5c6ebfc5fd5151db53b486856823b1e51)
![{\displaystyle \mathrm {B} (x,y)=\int _{0}^{\infty }{\frac {t^{x-1}}{(1+t)^{x+y}}}\,dt,\qquad {\mathrm {R} e}(x)>0,\ {\mathrm {R} e}(y)>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/392d889fdabf0557d2136b832fbbc2031c5193ba)
![{\displaystyle \mathrm {B} (x,y)={\frac {1}{y}}\sum _{n=0}^{\infty }(-1)^{n}{\frac {(x)_{n+1}}{n!(x+n)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a23213e61e9b935b14e94ca740f9b5de1da080ee)
nu mana (x)n nyaéta falling factorial.
Tempo ogé: integral Euler, falling factorial, fungsi gamma