Apostol volume 2 ex 1.17 prob 10
Let V be the linear space of all real functions f continuous on [0, + ∞ ) and such that the integral ∫ e ^(−t)f^2(t) dt converges. Define (f,g) =∫ e^(−t) f(t)g(t) dt. Let f(x)=e ^(-t) . Find the linear polynomial that is nearest to f.
**Note all integrals are from 0 to infinity.
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