, Triangulation of a spherical triangle using successive refinements, p.146

, A 3D walk avoiding the negative octant

, 3D walks avoiding a wedge

, suitably normalized) eigenfunction associated to ? 1 . In the particular case of 3D Brownian motion, if the cone K is an intersection of three halfspaces, the section C becomes a spherical triangle and the exponent in (5.40) is directly related to the principal eigenvalue of a spherical triangle

, First, the case of non-identity covariance matrices is easily reduced to the standard case, by applying a simple linear transform (notice, however, that this implies changing the initial cone, and therefore the domain of the Dirichlet problem). The situation is more subtle in the case of drifted Brownian motion: various asymptotic regimes exist

, let us mention the following: Singularity analysis. Is it possible to obtain similar results on non-D-finiteness of Hadamard models using the Hadamard product of generating functions? This would mean to prove Corollaries 69 and 73 directly

, This is clearly the model for which we can find the greatest number of estimations in the literature, 3D Kreweras model

, Costabel, vol.55, 2008.

, ? 5.159 by Ratzkin and Treibergs, vol.117, 2009.

, ? 5.1589 by Bostan, Raschel and Salvy, vol.33, 2012.

, ? 5.162 by Balakrishna, 2013.

, ? 5.1606 by Balakrishna, 2013.

, ? 5.1591452 by Bacher, Kauers and Yatchak, 2016.

, ? 5.159145642466 Guttmann, vol.88, 2017.

, ? 5.159145642470 by our result with a finite element method (see Section 5.7)

, What is the exact value? Is it a rational number? The triangle associated to Kreweras model

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, Fonctions génératrices