All Questions

Is it true that $$a_{k,n}:=\int_0^{2\pi}x^k\cos(nx)\,dx$$ is nonincreasing in natural $n$ for each $k\in\{0,1,\dots\}$? This question is related to this previous one. Twice integrating by parts, one ...

Let say a function $f$ is defined iteratively over the set of positive integers, for instance $f(t+1)=f(f(t))$ or $f(t+1)=f(t)+f(t-1)$. Based on the recurrence relationship and initial conditions, how ...

These are two possible definitions of antiderivative (integral) incorporating a supposedly natural choice of an integration constant (see this question for further details). The first one is based on ...