EOP (exceptional orthogonal polynomials)
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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 , with as above, with the weight function of (18.36.10), and 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 is a polynomial of order for , seemingly suggesting that for , 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.
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►These cases correspond to the two distinct orthogonality conditions of (18.35.6) and (18.35.6_3).
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