Geodesic
Negative moments of orthogonal polynomials
Forum of Mathematics, Sigma, Tome 11 (2023)

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If a sequence indexed by nonnegative integers satisfies a linear recurrence without constant terms, one can extend the indices of the sequence to negative integers using the recurrence. Recently, Cigler and Krattenthaler showed that the negative version of the number of bounded Dyck paths is the number of bounded alternating sequences. In this paper, we provide two methods to compute the negative versions of sequences related to moments of orthogonal polynomials. We give a combinatorial model for the negative version of the number of bounded Motzkin paths. We also prove two conjectures of Cigler and Krattenthaler on reciprocity between determinants. 
@article{10_1017_fms_2023_23,
     author = {Jihyeug Jang and Donghyun Kim and Jang Soo Kim and Minho Song and U-Keun Song},
     title = {Negative moments of orthogonal polynomials},
     journal = {Forum of Mathematics, Sigma},
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     year = {2023},
     doi = {10.1017/fms.2023.23},
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}
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Jihyeug Jang; Donghyun Kim; Jang Soo Kim; Minho Song; U-Keun Song. Negative moments of orthogonal polynomials. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.23

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