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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

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How to create a function whose harmonic is a sine wave [closed]

How do I solve the following equation for $f(\cdot)$? $f(x)+\frac{1}{n}f(nx)=\sin(x)$ That is, how do I create a function which, when combined with its nth harmonic, will be a sine wave?