Difference between revisions of "1/B(n,m)=n((n+m-1) choose (m-1))"
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(Created page with "==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 b...") |
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==References== | ==References== | ||
| − | * {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|prev=1/B(n,m)=m((n+m-1) choose (n-1))|next= | + | * {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|prev=1/B(n,m)=m((n+m-1) choose (n-1))|next=B(x,y)=2^(1-x-y)integral (1+t)^(x-1)(1-t)^(y-1)+(1+t)^(y-1)(1-t)^(x-1) dt}}: $\S 1.5 (9)$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Revision as of 23:06, 24 June 2017
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.
Proof
References
- 1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 1.5 (9)$
