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# Continuity of beta function. watch

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1. I need to make an assignment on beta function. So, I need to know about the continuity of beta function. would anyone be a dear to describe beta function and it's continuity and convergence ?
2. (Original post by S. M. Naser)
I need to make an assignment on beta function. So, I need to know about the continuity of beta function. would anyone be a dear to describe beta function and it's continuity and convergence ?
No. Although I do almost admire the blatant way you're asking someone else to do the work so you don't have to.
3. (Original post by DFranklin)
No. Although I do almost admire the blatant way you're asking someone else to do the work so you don't have to.
PRSOM!
4. (Original post by BuryMathsTutor)
PRSOM!
Sorry. Don't get me wrong. I have found the following things on continuity of beta function. I am not sure if the following proof is complete. I need to know details if there anything else.

Theorem:
Let x,y∈R

be real numbers.

Let B(x,y)

be the Beta function:

B(x,y):=∫→1→0tx−1(1−t) y−1 dt

Let y∈R>0

be given.

Then B(x,y)
is a positive and continuous function of x on R>0

.

Proof

For each x>0
, we have for all t with 0<t<1

that:

tx−1(1−t)y−1>0

from which it is immediate that B(x,y)>0
.

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Updated: January 11, 2019
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