(adsbygoogle = window.adsbygoogle || []).push({}); Do Orthogonal Polynomials have always real zeros ??

the idea is , do orthogonal polynomials [tex] p_{n} (x) [/tex] have always REAl zeros ?

for example n=2 there is a second order polynomial with 2 real zeros

if we consider that there is a self-adjoint operator L so [tex] L[p_{n} (x)]= \mu _{n} p_{n} (x) [/tex] if the orthogonal POLYNOMIALS are eigenfunctions of an operator with a real spectrum are ALL the zeros real ? , and if all the zeros are REAL can they be related to the spectrum of L ??

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# Do Orthogonal Polynomials have always real zeros ?

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