Paper Citation Record · LEDGER

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way

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Outbound references

Observation 6f1e4bf3-6d0f-4b29-b6c1-1cdcd2547145 · outbound

This paper cites Number 155.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Number 155

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.700717Z

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Observation 7155714a-94dc-4069-a21f-6274b9554589 · outbound

This paper cites Sur une famille de polynˆ omes ` a deux variables orthogonaux dans un triangle.Comptes rendus hebdomadaires des s´ eances de l’Acad´ emie des sciences, 245(26):2459–2461, 1957.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Sur une famille de polynˆ omes ` a deux variables orthogonaux dans un triangle.Comptes rendus hebdomadaires des s´ eances de l’Acad´ emie des sciences, 245(26):2459–2461, 1957

Reference 2

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Observation d217dd2a-824d-4b86-b851-28efa498ea07 · outbound

This paper cites Two-variable analogues of the classical orthogonal polynomials.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Two-variable analogues of the classical orthogonal polynomials

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.673896Z

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Observation 969f1bfd-c828-4c43-a2b3-c715a5d915e1 · outbound

This paper cites Spectral methods on triangles and other domains.Journal of Scientific Computing, 6:345–390, 1991.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Spectral methods on triangles and other domains.Journal of Scientific Computing, 6:345–390, 1991

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.654271Z

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Observation 1f58e507-3a9b-477a-b770-90aabe142299 · outbound

This paper cites Oxford University Press, 2005.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Oxford University Press, 2005

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T16:16:57.841235Z

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Observation 17653295-68bb-4f0f-bbfe-e66f7958f6b7 · outbound

This paper cites Orthogonal polynomials in two variables.Annali di Matematica Pura ed Applicata, 76:325–376, 1967.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Orthogonal polynomials in two variables.Annali di Matematica Pura ed Applicata, 76:325–376, 1967

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.625018Z

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Observation 8a219364-c4a1-4c5f-a2d8-2d6047910434 · outbound

This paper cites On some two-dimensional analogues of classical orthogonal polynomials.Latv.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way On some two-dimensional analogues of classical orthogonal polynomials.Latv

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.609898Z

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Observation a41a8ea6-a47d-46a8-9ff0-742320f4c2e1 · outbound

This paper cites Two-Dimensional Krall–Sheffer Polynomials and Quantum Systems on Spaces with Constant Curvature.Letters in Mathematical Physics, 65:83–94, 2003.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Two-Dimensional Krall–Sheffer Polynomials and Quantum Systems on Spaces with Constant Curvature.Letters in Mathematical Physics, 65:83–94, 2003

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.594623Z

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Observation ad3b97fc-dff0-4904-8e04-db559ab7eadb · outbound

This paper cites Symmetry algebra for the generic superintegrable system on the sphere.Journal of High Energy Physics, 2018(2), 2018.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Symmetry algebra for the generic superintegrable system on the sphere.Journal of High Energy Physics, 2018(2), 2018

Reference 9

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Observation d90dc958-b500-4a0c-9c85-7e39ef24d1b1 · outbound

This paper cites Hidden symmetry.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Hidden symmetry

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.563834Z

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Observation 81e10fa4-2456-42c9-a187-1b7511ce8cda · outbound

This paper cites Superintegrability in two dimensions and the Racah–Wilson algebra.Letters in Mathematical Physics, 104:931–952, 2014.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Superintegrability in two dimensions and the Racah–Wilson algebra.Letters in Mathematical Physics, 104:931–952, 2014

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.549058Z

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Observation b68802b2-73bb-416a-8971-17e1ccaa15a3 · outbound

This paper cites The Racah algebra and superintegrable models.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way The Racah algebra and superintegrable models

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.534022Z

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Observation 0bfeff11-4bbf-489a-a040-4e2c091ec79d · outbound

This paper cites Two linear transformations each tridiagonal with respect to an eigenbasis of the other.Linear algebra and its applications, 330(1-3):149–203, 2001.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Two linear transformations each tridiagonal with respect to an eigenbasis of the other.Linear algebra and its applications, 330(1-3):149–203, 2001

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.519423Z

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Observation 32fe9115-5ea5-4a24-8ad0-cefb0986fa37 · outbound

This paper cites A higher rank Racah algebra and theZ n 2 Laplace–Dunkl operator.Journal of Physics A: Mathematical and Theoretical, 51(2):025203, 2017.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way A higher rank Racah algebra and theZ n 2 Laplace–Dunkl operator.Journal of Physics A: Mathematical and Theoretical, 51(2):025203, 2017

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.504493Z

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Observation ef666e16-d885-4fe8-a18a-06a42e13440f · outbound

This paper cites Representations of the rank two Racah algebra and orthogonal multivariate polynomials.Linear Algebra and its Applications, 664:165–215, 2023.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Representations of the rank two Racah algebra and orthogonal multivariate polynomials.Linear Algebra and its Applications, 664:165–215, 2023

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.489653Z

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Observation 8e596922-61ae-4ebf-a943-0d53e6824445 · outbound

This paper cites Bispectrality of multivariable Racah–Wilson polynomials.Constructive Approximation, 31(3):417–457, 2010.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Bispectrality of multivariable Racah–Wilson polynomials.Constructive Approximation, 31(3):417–457, 2010

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.473420Z

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Observation e9272611-e220-40fc-bdb7-5cda7664ee86 · outbound

This paper cites Orthogonal polynomials with symmetry of order three.Canadian Journal of Mathematics, 36(4):685–717, 1984.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Orthogonal polynomials with symmetry of order three.Canadian Journal of Mathematics, 36(4):685–717, 1984

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.458041Z

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Observation fe6a282c-85e7-4ac4-9ba2-5fabadd6bce2 · outbound

This paper cites A difference equation and Hahn polynomials in two variables.Pacific Journal of Mathematics, 92(1):57–71, 1981.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way A difference equation and Hahn polynomials in two variables.Pacific Journal of Mathematics, 92(1):57–71, 1981

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.443153Z

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Observation b6873c19-526d-460d-9ab7-ef062d206a5f · outbound

This paper cites The rank two Jacobi algebra.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way The rank two Jacobi algebra

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-15T16:16:58.066896Z

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Observation 909412ce-5034-4162-91ff-0d8f9153c86d · outbound

This paper cites Tridiagonalization of the hypergeometric operator and the Racah–Wilson algebra.Proceedings of the American Mathematical Society, 144(10):4441– 4454, 2016.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Tridiagonalization of the hypergeometric operator and the Racah–Wilson algebra.Proceedings of the American Mathematical Society, 144(10):4441– 4454, 2016

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.428238Z

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Observation 1bd51d11-53cd-4da9-9778-0eee9301baa8 · outbound

This paper cites The Higgs and Hahn algebras from a Howe duality perspective.Physics Letters A, 383(14):1531–1535, 2019.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way The Higgs and Hahn algebras from a Howe duality perspective.Physics Letters A, 383(14):1531–1535, 2019

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.413165Z

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Observation b147ecab-4dd2-4ad4-b437-41ea923f652d · outbound

This paper cites Mutual integrability, quadratic algebras, and dynamical symmetry.Annals of Physics, 217(1):1–20, 1992.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Mutual integrability, quadratic algebras, and dynamical symmetry.Annals of Physics, 217(1):1–20, 1992

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.397644Z

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Observation de1917a6-a767-4577-8035-2beb6d107561 · outbound

This paper cites McGraw-Hill, 1953.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way McGraw-Hill, 1953

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.381452Z

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Observation 8b6c7cd9-4acb-411c-920a-e9530b8ffb23 · outbound

This paper cites Finite-dimensional irreducible modules of the Racah algebra at characteristic zero.SIGMA.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Finite-dimensional irreducible modules of the Racah algebra at characteristic zero.SIGMA

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.364961Z

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Observation f8bdea7e-02e0-4304-a494-a1c26c6e4056 · outbound

This paper cites Springer, 2010.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Springer, 2010

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.348594Z

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Observation b51d1dd9-6025-4c22-b741-77c56661bb3c · outbound

This paper cites Realisations of Racah algebras using Jacobi operators and convo- lution identities.Advances in Applied Mathematics, 153:102620, 2024.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Realisations of Racah algebras using Jacobi operators and convo- lution identities.Advances in Applied Mathematics, 153:102620, 2024

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.333755Z

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Observation 45b08e83-b518-4408-98f0-c73489eab889 · outbound

This paper cites An identity satisfied by the Racah coefficients.Journal of Mathematics and Physics, 31(1-4):287–293, 1952.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way An identity satisfied by the Racah coefficients.Journal of Mathematics and Physics, 31(1-4):287–293, 1952

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.317950Z

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Observation a224c402-fd7d-4263-b67c-971335754755 · outbound

This paper cites Theoretical studies in nuclear structure v.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Theoretical studies in nuclear structure v

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.301770Z

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Observation 495a5326-811e-4c8e-807f-b95a618f2d8a · outbound

This paper cites Introduction to Leonard pairs.Journal of Computational and Applied mathematics, 153(1- 2):463–475, 2003.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Introduction to Leonard pairs.Journal of Computational and Applied mathematics, 153(1- 2):463–475, 2003

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.286083Z

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Observation 77aa947b-119b-430a-a24b-adfbb10e4969 · outbound

This paper cites FactorizedA2-Leonard pair.The Ramanujan Journal, 66(2):25, 2025.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way FactorizedA2-Leonard pair.The Ramanujan Journal, 66(2):25, 2025

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.269001Z

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Observation c6b07bc8-accd-43fa-a65d-757973224125 · outbound

This paper cites Classical and quantum conformal field theory.Communications in Math- ematical Physics, 123(2):177–254, 1989.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Classical and quantum conformal field theory.Communications in Math- ematical Physics, 123(2):177–254, 1989

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.253888Z

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Observation 2fc220f9-f882-4f73-ac67-92c577aaf25c · outbound

This paper cites Invariants of 3-manifolds via link polynomials and quantum groups.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Invariants of 3-manifolds via link polynomials and quantum groups

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.238834Z

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Observation bbcc135f-0f05-4443-bd57-b07c0d3d6651 · outbound

This paper cites de Gruyter, 2010.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way de Gruyter, 2010

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.223530Z

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Observation 197c1e27-7577-4c2c-8678-0a7287797705 · outbound

This paper cites Two-variable orthogonal polynomials of big q-Jacobi type.Journal of computational and applied mathematics, 233(6):1554–1561, 2010.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Two-variable orthogonal polynomials of big q-Jacobi type.Journal of computational and applied mathematics, 233(6):1554–1561, 2010

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.208446Z

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Observation 33bfd786-48cf-4d08-b00f-8583497e93c3 · outbound

This paper cites Two-variable−1 Jacobi polynomials.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Two-variable−1 Jacobi polynomials

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.191329Z

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Observation 654b2a1c-9866-44a6-b222-909b3d66714b · outbound

This paper cites The Askey–Wilson algebra and its avatars.Journal of Physics A: Mathematical and Theoretical, 54(6):063001, 2021.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way The Askey–Wilson algebra and its avatars.Journal of Physics A: Mathematical and Theoretical, 54(6):063001, 2021

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.173036Z

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Observation fd06a646-3b19-49d2-9068-a61cf16bd556 · outbound

This paper cites Dunkl shift operators and Bannai–Ito polynomials.Ad- vances in Mathematics, 229(4):2123–2158, 2012.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Dunkl shift operators and Bannai–Ito polynomials.Ad- vances in Mathematics, 229(4):2123–2158, 2012

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.154729Z

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Observation 02b6e8e7-b27f-4693-8ea0-e4d7472f4f14 · outbound

This paper cites The Bannai-Ito algebra and some applications.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way The Bannai-Ito algebra and some applications

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.138112Z

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Observation 4005b435-1c4b-42d4-bf65-e2dc57dd3ad7 · outbound

This paper cites Exact solvabilityof the Calogero and Sutherland models.Modern Physics Letters A, 10(29):2213–2221, 19955.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Exact solvabilityof the Calogero and Sutherland models.Modern Physics Letters A, 10(29):2213–2221, 19955

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.121304Z

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Observation 6e215e1a-bb04-4939-ba5a-8891210e7f1d · outbound

This paper cites Racah algebras, the centralizer Zn(sl2)and its Hilbert-Poincar´ e series.Annales Henri Poincar´ e, 23:2657–2682, 2022.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way Racah algebras, the centralizer Zn(sl2)and its Hilbert-Poincar´ e series.Annales Henri Poincar´ e, 23:2657–2682, 2022

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.103865Z

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Observation 54b9cf29-6f85-4dd7-a48f-a9074ec0e121 · outbound

This paper cites The Racah algebra of rank 2: Properties, symmetries and representation.

Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way The Racah algebra of rank 2: Properties, symmetries and representation

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:16:58.086301Z

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Pith citing papers

Observation 2612c951-50ca-417d-8ac2-c665b4d60014 · inbound

Realization embeddings of the rank two Racah algebra into the rank two Jacobi algebra cites this paper.

Realization embeddings of the rank two Racah algebra into the rank two Jacobi algebra Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T08:41:39.203439Z

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