1/B(n,m)=n((n+m-1) choose (m-1))

Theorem

The following formula holds: $$\dfrac{1}{B(n,m)} = n {{n+m-1} \choose {m-1}},$$ where $B$ denotes the beta function and ${{n+m-1} \choose {m-1}}$ denotes a binomial coefficient.

References

• 1953: Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger and Francesco G. Tricomi: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 1.5 (9)$