Where's my Gamma!-II

Calculus Level 1

Evaluate

Γ ( 2 ) × Γ ( 3 ) \Large\Gamma (2) \times \Large\Gamma( 3)

Here Γ \Gamma represents the gamma function.


The answer is 2.

Swapnil Das by Swapnil Das , 20, India

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2 solutions

Akhil Bansal
Oct 8, 2015

Γ ( n ) = ( n − 1 ) ! \Large \Gamma (n) = (n - 1)!

Γ ( 2 ) × Γ ( 3 ) = 1 ! × 2 ! = 2 \Gamma (\color{#D61F06}2) \times \Gamma (\color{#3D99F6}3) = \color{#D61F06}1! \times \color{#3D99F6}2! = \color{#69047E}2

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Oon Han
Dec 11, 2017

Using the fact that: Γ ( x ) = ( x − 1 ) ! \Gamma (x)=(x-1)! we can show that: Γ ( 2 ) × Γ ( 3 ) = ( 2 − 1 ) ! × ( 3 − 1 ) ! = 1 ! × 2 ! = 1 × ( 2 × 1 ) = 2 \Gamma (2)\times \Gamma (3)=(2-1)!\times (3-1)!=1!\times 2!=1\times (2\times 1)= \color{#D61F06}{2}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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