Thread: part of inverse gamma

1. part of inverse gamma

is it possible to go from
$
exp[-\frac{1}{2}(\frac{s + n\mu^2 - 2n\mu \overline{y} + \overline{y^2}n)}{\sigma^2 c} ]
$

to

$
exp [\frac {s + n\overline{y^2}(\frac{1/c}{n + 1/c})}{2\sigma^2}]$

?

(because Im trying to make my beta equal to the last part)

or am i just wasting my time trying to make this work?

because i tried, and i can't