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Notes on Umemura polynomials
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 5, pp. 1091-1118.

Nous donnons un survol des polynômes spéciaux associés aux solutions algébriques de la sixième équation de Painlevé, et formulons une conjecture concernant une formule combinatoire pour les polynômes d’Umemura associés à une classe de solutions algébriques de P VI avec deux paramètres discrets.

We give a survey on special polynomials associated with algebraic solutions of the sixth Painlevé equation, and formulate a conjecture regarding a combinatorial formula for Umemura polynomials associated with a class of algebraic solutions of P VI with two discrete parameters.

Publié le :
DOI : https://doi.org/10.5802/afst.1658
Classification : 33C45,  05E35,  34M55
Mots clés : Umemura polynomial, Painlevé equation, Toda equation, special polynomial
@article{AFST_2020_6_29_5_1091_0,
     author = {Masatoshi Noumi},
     title = {Notes on {Umemura} polynomials},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {1091--1118},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 29},
     number = {5},
     year = {2020},
     doi = {10.5802/afst.1658},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1658/}
}
Masatoshi Noumi. Notes on Umemura polynomials. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 5, pp. 1091-1118. doi : 10.5802/afst.1658. https://afst.centre-mersenne.org/articles/10.5802/afst.1658/

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