MathDB

Answer either (i) or (ii):
(i) Prove that

\sum_{n=2}^{\infty} \frac{\cos (\log \log n)}{\log n}

diverges.
(ii) Assume that

p>0, a>0

, and

ac-b^{2} >0,

and show that \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \frac{ dx\; dy}{(p+ax^2 +2bxy+ cy^2 )^{2}}= \pi p^{-1} (ac-b^{2})^{- 1\slash 2}.

Problem Statement