Timeline for Infinite sum of reciprocals of squares of lengths of tangents from origin to the curve $y=\sin x$

10 events

when toggle format	what		by	license	comment
Sep 25, 2018 at 21:01	answer	added	Andreas Rüdinger		timeline score: 2
Sep 25, 2018 at 18:37	comment	added	Max Alekseyev		@Qfwfq: The question can be posed as summing of $g(z)=\frac{1+z^2}{z^2(z^2+2)}$ over the zeros of $f(z)=\frac{\sin(z)-z\cos(z)}{z^3}$, or alike. The hope is that under an appropriate choice of $f(z)$ and $g(z)$, one can use the residue theorem to evaluate the sum.
Sep 25, 2018 at 18:26	comment	added	LSpice		Reading your title is an adventure.
Sep 25, 2018 at 18:22	comment	added	Qfwfq		@Count Iblis: how is that related to the question?
Sep 25, 2018 at 17:54	answer	added	Max Alekseyev		timeline score: 3
Sep 25, 2018 at 16:46	comment	added	Count Iblis		If $$\oint_{C(R)}\frac{f'(z)}{f(z)}g(z) dz$$ with the contour $C(R)$ a circle of radius $R$ with center the origin, tends to zero for $R\to\infty$, then the residue theorem (if applicable), yields a relation between the summation of $g(z)$ over the zeros of $f(z)$ in terms of the residues of the integrand at the poles of $g(z)$.
Sep 25, 2018 at 14:15	history	edited	Rohan Shinde	CC BY-SA 4.0	added 8 characters in body
Sep 25, 2018 at 8:37	history	edited	Alex M.		edited tags
Sep 25, 2018 at 8:30	review	First posts
Sep 25, 2018 at 8:32
Sep 25, 2018 at 8:29	history	asked	Rohan Shinde	CC BY-SA 4.0