B(x,y+1)=(y/x)B(x+1,y)

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Theorem

The following formula holds: $$B(x,y+1)=\dfrac{y}{x} B(x+1,y),$$ where $B$ denotes the beta function.

Proof

References

1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 1.5 (6)$

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