Is this known yet? (an expression for the Beta Function I have not yet seen)

  • #1
PhysicsRock
37
4
So, I've recently played around a little with the Gamma Function and eventually managed to find an expression for the Beta Function I have not yet seen. So I'm asking you guys, if you've ever seen this expression somewhere or if this is a new thing. Would be cool if it was, so here's the formula:
$$
B(x,y) = \frac{\Gamma(x)}{x} \cdot \left( \sum_{k=1}^{y} \frac{\Gamma(x+y-k)}{\Gamma(y-k+1)} \right)^{-1}
$$

Obviously, this only works for non-negative integer pairs of ##x## and ##y##. Still pretty interesting I think.
 

Answers and Replies

  • #2
fresh_42
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Sure you have ##y## as upper bound of the sum?

Anyway, it looks very similar to ##B(x,y)=\dfrac{(x-1)!(y-1)!}{(x+y-1)!}##
 
  • #3
PhysicsRock
37
4
Sure you have ##y## as upper bound of the sum?

Anyway, it looks very similar to ##B(x,y)=\dfrac{(x-1)!(y-1)!}{(x+y-1)!}##
Yes, ##y## is definitely the upper bound.
 

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