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Let $k$ be an integer and consider the function $$ f(t)=\prod_{i=1}^{k} \cos(3^{i-1}\pi t). $$ I'm interested in finding bounds for $\int_{0}^{1}|f(t)|dt$ in terms of $k$. The first idea that comes to ...

Recall the $j$-invariant function, namely, $$ j(\tau)=\frac{1}{q}+\sum_{k\geq 0}c_kq^k, $$ where $q=e^{2\pi i \tau}$ and the coefficients $(c_k)_k$ are in the OEIS sequence A000521. By using some ...

Stationary phase method (in the usual setup) gives asymptotic for $$ I(\lambda)=\int_{a}^{b} f(t) e^{i \lambda \varphi(t)} d t, $$ when at any stationary point $x_0$ ($\varphi'(x_0)=0$) second ...

Let me preface this question by saying that I am not exactly sure it counts as research level. It is crossposted on mathstackexchange: https://math.stackexchange.com/questions/1519724/integrating-a-...