# EOP (exceptional orthogonal polynomials)

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## 4 matching pages

##### 1: 18.1 Notation

##### 2: 18.36 Miscellaneous Polynomials

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###### §18.36(vi) Exceptional Orthogonal Polynomials

…##### 3: 18.39 Applications in the Physical Sciences

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►c) A Rational SUSY Potential
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►and eigenvalues $n+3$, with $n$ as above, with $w(x)$ the weight function of (18.36.10), and ${\widehat{H}}_{n+3}\left(x\right)$ a type III Hermite EOP defined by (18.36.8) and (18.36.9).
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►This seems odd at first glance as ${\widehat{H}}_{n+3}\left(x\right)$ is a polynomial of order $n+3$ for $n=0,1,2,\mathrm{\dots}$, seemingly suggesting that for $n=0$, this being the first excited state, i.
…Kuijlaars and Milson (2015, §1) refer to these, in this case complex zeros, as

*exceptional*, as opposed to*regular*, zeros of the EOP’s, these latter belonging to the (real) orthogonality integration range. … ►These cases correspond to the two distinct orthogonality conditions of (18.35.6) and (18.35.6_3). …