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- W4315706766 abstract "We consider the complex $nu$ plane structure of the associated Legendre function of the second kind $Q^{-1/2-K}_{nu}(coshrho)$. We find that for any noninteger value for $K$ $Q^{-1/2-K}_{nu}(coshrho)$ has an infinite number of poles in the complex $nu$ plane, but for any negative integer $K$ there are no poles at all. For $K=0$ or any positive integer $K$ there is only a finite number of poles, with there only being one single pole (at $nu=0$) when $K=0$. This pattern is characteristic of the exceptional points that appear in a wide variety of physical contexts. However, unusually for theories with exceptional points, $Q^{-1/2-K}_{nu}(coshrho)$ has an infinite number of them. Other than in the $PT$-symmetry Jordan-block case, exceptional points usually occur at complex values of parameters. While not being Jordan-block exceptional points themselves, the exceptional points associated with the $Q^{-1/2-K}_{nu}(coshrho)$ nonetheless occur at real values of $K$." @default.
- W4315706766 created "2023-01-12" @default.
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- W4315706766 date "2023-01-08" @default.
- W4315706766 modified "2023-09-26" @default.
- W4315706766 title "Exceptional points for associated Legendre functions of the second kind" @default.
- W4315706766 doi "https://doi.org/10.48550/arxiv.2301.04092" @default.
- W4315706766 hasPublicationYear "2023" @default.
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