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单词 AlternateIntegralRepresentationOfBetaFunction
释义

alternate integral representation of beta function


By making the change of variable xp=y, we see that

01xp-1(1-x)q-1𝑑x=1p01(1-y1p)q-1𝑑y.

Hence, we have

01(1-y1p)q-1𝑑y=pΓ(p)Γ(q)Γ(p+q).
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