Testwiki:Reference desk/Archives/Mathematics/2018 August 7

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August 7

Fourier series question

How do I get the Fourier series expansion for ${\text{cosec}}^2(nx)$? I've tried doing the integrals with Mathematica, but they look unreasonably ugly.--Leon (talk) 13:06, 7 August 2018 (UTC)

It's been a while, but $f(x)={\csc }^{2}x$ is not a square-integrable function (over $[0,2\pi ]$ say), so it doesn't have a Fourier series. –Deacon Vorbis (carbon • videos) 14:57, 7 August 2018 (UTC)

Ah. Thanks.--Leon (talk) 15:42, 7 August 2018 (UTC)

Distance on an oblate spheroid

On a normal spheroid, the distance between two points along the surface is relatively trivial to compute. But is there a closed form solution for the same problem on an oblate spheroid like the earth? For the purposes of this, "closed form" can include elliptic integrals, and I have this feeling that will be necessary.--Jasper Deng (talk) 17:54, 7 August 2018 (UTC)

See Geodesics on an ellipsoid --catslash (talk) 19:28, 7 August 2018 (UTC)