Hypergeometric solutions to the q-painlevé equations

Hypergeometric solutions to seven q-Painleve equations in Sakai's classification are constructed. Geometry of plane curves is used to reduce the q-Painleve equations to the three-term recurrence relations for q-hypergeometric functions.

[1]  Mizan Rahman,et al.  Basic Hypergeometric Series , 1990 .

[2]  Y. Ohta,et al.  An affine Weyl group approach to the eight-parameter discrete Painlevé equation , 2001 .

[3]  H. Sakai,et al.  Riccati solutions of discrete Painlevé equations with Weyl group symmetry of type E8(1) , 2002, nlin/0210040.

[4]  K. M. Tamizhmani,et al.  Special function solutions of the discrete painlevé equations , 2001 .

[5]  D. Masson,et al.  Contiguous relations, basic hypergeometric functions, and orthogonal polynomials. II. Associated big q-Jacobi polynomials , 1992 .

[6]  Masaaki Yoshida,et al.  From Gauss to Painlevé , 1991 .

[7]  K. Kajiwara,et al.  A study on the fourth q-Painlevé equation , 2000, nlin/0012063.

[8]  M. Jimbo,et al.  A q-analog of the sixth Painlevé equation , 1995, chao-dyn/9507010.

[9]  D. Masson,et al.  Contiguous relations, continued fractions and orthogonality , 1995, math/9511218.

[10]  A. Ramani,et al.  Discrete Painlevé equations: coalescences, limits and degeneracies , 1995, solv-int/9510011.

[11]  T. Koornwinder,et al.  BASIC HYPERGEOMETRIC SERIES (Encyclopedia of Mathematics and its Applications) , 1991 .

[12]  Mizan Rahman,et al.  The associated Askey-Wilson polynomials , 1991 .

[13]  Rene F. Swarttouw,et al.  The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue Report Fac , 1996, math/9602214.

[14]  Y. Ohta,et al.  10E9 solution to the elliptic Painlevé equation , 2003 .

[15]  H. Sakai.  Casorati determinant solutions for the q-difference sixth Painlevé equation , 1998 .

[16]  On a q-Difference Painlevé III Equation: I. Derivation, Symmetry and Riccati Type Solutions , 2002, nlin/0205019.

[17]  Y. Ohta,et al.  The q-Painlevé V equation and its geometrical description , 2001 .

[18]  H. Sakai,et al.  Rational Surfaces Associated with Affine Root Systems¶and Geometry of the Painlevé Equations , 2001 .