Bilinear Structure and Exact Solutions of the Discrete Painlev\'e I   Equation
  Bilinear structure for the discrete Painlev\'e I equation is investigated. The solution on semi-infinite lattice is given in terms of the Casorati determinant of discrete Airy function. Based on this fact, the discrete Painlev\'e I equation is naturally extended to a discrete coupled system. Corresponding matrix model is also mentioned. 
Y.Ohta(Dept. Appl. Math., Hiroshima Univ.), K.Kajiwara(Dept. Elecrical   Eng., Doshisha Univ.), and J.Satsuma(Dept. Math. Sc...