(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm trying to prove that the random variable with t distribution with k degrees of freedom will have N(0,1) as k→∞ the two equations below are derived from the pdf of the t-distribution:

2. Relevant equations which I can't get my head around

[tex]lim_{k\to\infty}((1+\frac{x^2}{k})^k)^{-0.5} = e^{-\frac{x}{2}}[/tex]

3. The attempt at a solution

I have proved [tex]lim_{k\to\infty}((1+\frac{x^2}{k})^{-0.5}=1 [/tex], which I admit wasn't too hard.

The statement involving the limit of gamma function was given to us as "knowing that it can be shown" but I would appreciate if someone was willing to explain it/point me to the source where I can find it.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Limit question: from proof that t-distribution approaches N(0,1)

**Physics Forums | Science Articles, Homework Help, Discussion**