A holonomic system is a system of linear partial differential equations with a finite-dimensional space of local solutions at a generic nonsingular point. The dimension of this space is the holonomic rank. Generic bivariate Horn systems are holonomic (Dickenstein et al. 2005). Holonomic systems can be represented locally by first-order Pfaffian systems (Saito et al. 2000).
Holonomic System
See also
Holonomic Function, Holonomic Rank, Horn System, Linear Partial Differential Equation, Partial Differential Equation, Pfaffian SystemExplore with Wolfram|Alpha
References
Dickenstein, A.; Matusevich, L. F.; and Sadykov, T. "Bivariate Hypergeometric D-Modules." Adv. Math. 196, 78-123, 2005. https://doi.org/10.1016/j.aim.2004.08.012.Saito, M.; Sturmfels, B.; and Takayama, N. Gröbner Deformations of Hypergeometric Differential Equations. Berlin, Germany: Springer-Verlag, 2000.Cite this as:
Weisstein, Eric W. "Holonomic System." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HolonomicSystem.html