We define the functions, $f_n$, $n=0,1,2,3,...,$ on $[-1,1]$ by $$f_n(x)=x^n$$
Then I have to find the inner product for $\langle f_n,f_m \rangle$ for all values of $n, m$ and I have in particular, to show that: $$||f_n||=(n+\frac{1}{2})^{-\frac{1}{2}}$$
But I'm not sure how to do that? I'm confused, what is m? I think to show the norm I have to use $||f_n||=\sqrt{\langle f_n|f_n\rangle}$ ? But how do I find the inner product and use it finding the norm? I hope anyone can help me?