B(x,y)B(x+y,z)=B(z,x)B(x+z,y)

Theorem

The following formula holds: $$B(x,y)B(x+y,z)=B(z,x)B(x+z,y),$$ where $B$ denotes the beta function.

References

• 1953: Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger and Francesco G. Tricomi: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 1.5 (7)$