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Closed form solution for $\int_{0}^{2\pi}|\cos^N x||\sin^M x|\cos^n x\sin^m x dx$
I am trying to calculate Fourier series coefficients (by hand) and the integrals I need to solve are of the following type
$$I(N,M,n,m)=\int_{0}^{2\pi}|\cos^N x||\sin^M x|\cos^n x\sin^m x dx,$$
in ...
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3
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Two complementary continued fractions that are algebraic numbers
Define the two similar continued fractions,
$$x=\cfrac{1}{km\color{blue}+\cfrac{(m-1)(m+1)} {3km\color{blue}+\cfrac{(2m-1)(2m+1)}{5km\color{blue}+\cfrac{(3m-1)(3m+1)}{7km\color{blue}+\ddots}}}}\tag1$$...
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