Stirling's Approximation for a factorial raised to a power

[rmiller70015]

Homework Statement

Find Stirling's Approximation for $[(\alpha - 1)!]^2$

Relevant Equations

For large N: $log(N!) \approx Nlog(N)-N$

Using log identities:
$log((\alpha - 1)!^2) = 2(log(\alpha - 1)!)$
Then apply Stirling's Approximation
$(2[(\alpha - 1)log(\alpha - 1) - (\alpha - 1)$
$= 2(\alpha -1)log(\alpha -1) - 2\alpha+2$

Is this correct? I can't find a way to check this computationally.

 

[Mark44]

Homework Statement:: Find Stirling's Approximation for $[(\alpha - 1)!]^2$
Relevant Equations:: For large N: $log(N!) \approx Nlog(N)-N$

Using log identities:
$log((\alpha - 1)!^2) = 2(log(\alpha - 1)!)$
Then apply Stirling's Approximation
$(2[(\alpha - 1)log(\alpha - 1) - (\alpha - 1)$
$= 2(\alpha -1)log(\alpha -1) - 2\alpha+2$

Is this correct? I can't find a way to check this computationally.

I don't think it's correct, and I get something different. If you want to approximate $[(\alpha - 1)!]^2$, first use Stirling's to approximate $(\alpha - 1)!$, and then square that result.

 

[rmiller70015]

Thanks, that was bugging me.