- #1
Gerenuk
- 1,034
- 5
I wonder:
Is it possible to find a function f(x) which satisfies this integral for *arbitrary* parameters a,b (but maybe of known domain)?
[tex]\int_{-\infty}^\infty e^{-x^2}f(ax+b)\mathrm{d}x=0[/tex]
I want [tex]f(\pm\infty)=0[/tex] and I can deduce
[tex]\int_{-\infty}^\infty x^n e^{-x^2}f^{(m)}(ax+b)\mathrm{d}x=0[/tex]
It would have to be oscillary I guess?!
Is it possible to find a function f(x) which satisfies this integral for *arbitrary* parameters a,b (but maybe of known domain)?
[tex]\int_{-\infty}^\infty e^{-x^2}f(ax+b)\mathrm{d}x=0[/tex]
I want [tex]f(\pm\infty)=0[/tex] and I can deduce
[tex]\int_{-\infty}^\infty x^n e^{-x^2}f^{(m)}(ax+b)\mathrm{d}x=0[/tex]
It would have to be oscillary I guess?!
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