Difference between revisions of "B(x,y)=integral (t^(x-1)+t^(y-1))(1+t)^(-x-y) dt"
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(Created page with "==Theorem== The following formula holds: $$B(x,y) = \displaystyle\int_0^1 (t^{x-1}+t^{y-1})(1+t)^{-x-y} \mathrm{d}t,$$ where $B$ denotes the beta function. ==Proof== ==R...") |
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==References== | ==References== | ||
| + | * {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|prev=Beta as improper integral|next=Beta is symmetric}}: $\S 1.5 (3)$ | ||
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Revision as of 22:51, 24 June 2017
Theorem
The following formula holds: $$B(x,y) = \displaystyle\int_0^1 (t^{x-1}+t^{y-1})(1+t)^{-x-y} \mathrm{d}t,$$ where $B$ denotes the beta function.
Proof
References
- 1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 1.5 (3)$
