average deviratives

Kémelli

Hi dear friends!

We have an interesting question, namely: Is the following sequence possible to construct?

"int_0^L f(x) w0(x) dx = L * <f(x)> " "int_0^L f(x) w1(x) dx = L * <df(x)/dx> " "int_0^L f(x) w2(x) dx = L * <d^2f(x)/dx^2> " ,,, and so on

where w0=1, w1, w2,... are orthogonal polynomials, with w1 of 1 degree, w2 of 2 degree, etc, and f is a function.

Thank you very much, Kémelli