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An explicit calculation of the Ronkin function
Johannes Lundqvist
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 2, p. 227-250

We calculate the second order derivatives of the Ronkin function in the case of an affine linear polynomial in three variables and give an expression of them in terms of complete elliptic integrals and hypergeometric functions. This gives a semi-explicit expression of the associated Monge-Ampère measure, the Ronkin measure.

Nous calculons les dérivées secondes de la fonction de Ronkin dans le cas d’un polynôme linéaire affine à trois variables, et nous donnons une expression de ces dérivées en termes d’intégrales elliptiques complètes et fonctions hypergéométriques. Cela donne une expression semi-explicite de la mesure de Monge-Ampère associée, la mesure de Ronkin.

Received : 2013-06-24
Accepted : 2014-11-18
Published online : 2015-05-27
DOI : https://doi.org/10.5802/afst.1447
@article{AFST_2015_6_24_2_227_0,
     author = {Johannes Lundqvist},
     title = {An explicit calculation of the Ronkin function},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 24},
     number = {2},
     year = {2015},
     pages = {227-250},
     doi = {10.5802/afst.1447},
     zbl = {1333.32010},
     mrnumber = {3358612},
     language = {en},
     url = {https://afst.centre-mersenne.org/item/AFST_2015_6_24_2_227_0}
}
Lundqvist, Johannes. An explicit calculation of the Ronkin function. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 2, pp. 227-250. doi : 10.5802/afst.1447. afst.centre-mersenne.org/item/AFST_2015_6_24_2_227_0/

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