Mathematical Enigma- XVIII

Calculus Level 3

Compute $B(3,4)$ , where $B(x,y)$ represents the Beta function.

If the answer is in the form $\frac{a}{b}$ ,where $a$ and $b$ are positive co prime integers, find $a+b$ .

1 solution

Swapnil Das
Nov 25, 2015

There's a unique relation between Beta and Gamma Function,

$B(x,y) = \frac { \Gamma (x)\Gamma (y) }{ \Gamma (x+y) }$ .

This gives $B(3,4)= \frac { \Gamma (3)\Gamma (4) }{ \Gamma (7) } =\frac { 2!3! }{ 6! } =\frac { 1 }{ 60 }$ .