no. 5
Notes on Umemura polynomials
Noumi, Masatoshi1
1 Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan
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 : 10.5802/afst.1658
Classification : 33C45, 05E35, 34M55
Mots clés : Umemura polynomial, Painlevé equation, Toda equation, special polynomial
Noumi, Masatoshi 1

1 Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan 
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Noumi, Masatoshi. 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. http://www.numdam.org/articles/10.5802/afst.1658/

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