Question

Express
dx in terms of Beta function, where m > 0, n >0; a > 0, 6 > 0.
(a + bx)"+n
[Hint. Put bx = az]​

Answer 1

Answer:

known that B(x,y)=∫∞0tx−1(1+t)x+ydt. From that we can obtain another great formula for the Beta Function which is

B(x,y)=∫10tx−1+ty−1(1+t)x+ydt

The proof is easy and it goes along these lines.

B(x,y)=∫∞0tx−1(1+t)x+ydt=∫10tx−1(1+t)x+ydt+∫∞1tx−1(1+t)x+ydt===u=1/t∫10tx−1(1+t)x+ydt+

Step-by-step explanation:

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