Revision as of 05:53, 6 June 2016

The beta function $B$ (note: $B$ is capital $\beta$ in Greek) is defined by the formula $$B(x,y)=\displaystyle\int_0^1 t^{x-1}(1-t)^{y-1}dt.$$

Properties

Theorem: $B(x,y)=B(y,x)$

Proof: █

Theorem: (i) $B(x+1,y)=\dfrac{x}{x+y} B(x,y)$
(ii) $B(x,y+1)=\dfrac{y}{x+y}B(x,y)$

Proof: █

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+[[Partial derivative of beta function]]
+[[Beta in terms of gamma]]
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+[[Beta in terms of sine and cosine]]
-{{:Beta in terms of sine and cosine}}
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