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Integral equation $\int_0^{2 \pi} \frac{1}{\sqrt{1+R^2 \sin^2(x)}}f(R \cos(x)) d x = 1$

Can we confirm that there does not exist a function $f$, which pleases this formula for all $R>0$: $$\int_0^{2 \pi} \frac{1}{\sqrt{1+R^2 \sin^2(x)}} f(R \cos(x))\, dx= 1.$$

2
math integral-equations
Marc Palm 2022-07-25 20:47:102022-07-25T08:07:10+02:00
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Answers: 0

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