Question on orthogonal function with respect to weight.

[yungman]

If F(x) and G(x) is orthogonal with respect to weight W(x), does this mean F(x) and G(x) are not necessary orthogonal by themselves?

$$\int$$F(x)G(x)W(x)dx=0 do not mean $$\int$$F(x)G(x)dx=0

If $$\int$$F(x)G(x)dx=0 then W(x)=1

Thanks

Alan

 

[marcusl]

Yes, correct on both items.

 

[yungman]

Thanks.
Alan