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- Problem Statement
- Does there exist a function ##f \in L_2[0,1]## such that for all natural ##n##, we have $$\int_0^1 x^n f(x) \, dx = 1$$

- Relevant Equations
- Nothing comes to mind.

At first I was thinking about using the dirac delta function ##\delta(x-1)##, but then I recalled ##\delta \notin L_2[0,1]##. Any ideas? I'm thinking no such function exists.