hypergeon1 http://www.math.kobe-u.ac.jp/OCD/hypergeon1.tfb 2003-07-30 experimental 2002-07-30, 2003-11-30 1 1 hypergeon0 arith1 fns1 interval1 linalg1 linalg4 relation1 set1 This CD defines symbols for A-hypergeometric series falling_factorial falling_factorial(n,i) is equal to n*(n-1)* ... *(n-i+1). raising_multi_factorial raising_multi_factorial is a product of pochhammer symbols. 2-ary function. reference: authors: "Saito, Sturmfels, Takayama" title: "Grobner Deformations of Hypergeometric Differential Equations" pages: 127 $ [v]_{u_+} = \prod_{i \in \Z\cap[0,n] :\ u_i > 0} (v_i+1)_{u_i} $ 1 0 1 falling_multi_factorial falling_multi_factorial is a product of falling pochhammer symbols. 2-ary function. reference: authors: "Saito, Sturmfels, Takayama" title: "Grobner Deformations of Hypergeometric Differential Equations" pages: 127 $ [v]_{u_-} = \prod_{i \in \Z\cap[0,n] :\ u_i < 0} v_i (v_i-1) \cdots (v_i + u_i-1) $ 1 0 a_hypergeomeric A-hypergeometric series reference: authors: "Saito, Sturmfels, Takayama" title: "Grobner Deformations of Hypergeometric Differential Equations" pages: 127 $ \phi(A,v,x) = \sum_{u \in \kernel{\Z^n \stackrel \Z^d}} \frac{[v]_{u_-}}{[v+u]_{u_+}} x^{v+u} $