All right, so I was wondering... I took a look at generating orthogonal functions (over an interval), and say I have these four:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{1}{\sqrt{3}}[/tex]

[tex]\frac{5}{3} - \frac{2}{3} x[/tex]

[tex]\frac{11}{3} \sqrt{\frac{5}{3}} - \frac{10}{3} \sqrt{\frac{5}{3}} x + \frac{2}{3} \sqrt{\frac{5}{3}} x^2[/tex]

[tex]\frac{245}{27} \sqrt{\frac{7}{3}} - \frac{116}{9} \sqrt{\frac{7}{3}} x + \frac{50}{9} \sqrt{\frac{7}{3}} x^2 - \frac{20}{27} \sqrt{\frac{7}{3}} x^3[/tex]

These four polynomials are all orthonormal and orthogonal over the interval [1,4]. Now what I want to know is, is it possible to prove that these are the ONLY polynomials of degree 3 or fewer that satisfy orthonormality and orthogonality?

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# Question about orthogonal functions

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