I am trying to construct functions $f\in C^\infty[1;\infty)\cap L^1[1;\infty)$ such that $\int_1^\infty f(t)dt=1$ and $\int_1^\infty t^kf(t)dt=0$ for all $k=1,2,3,\ldots$.
I have no idea, does anyone know how and help to construct those functions?
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An example (shifted by 1) is the Stiltjes ghost function. – you can call me Al Jan 22 '14 at 22:50