Riccati Solutions of Discrete Painlevé Equations with Weyl Group Symmetry of Type $E_8^{(1)}$

Details Riccati Solutions of Discrete Painlevé Equations with Weyl Group Symmetry of Type $E_8^{(1)}$ Riccati Solutions of Discrete Painlevé Equations with Weyl Group Symmetry of Type $E_8^{(1)}$

2002-10-18

arxiv.org/abs/nlin/0210040v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

22 pages

Scientific paper

We present a special solutions of the discrete Painlev\'e equations associated with $A_0^{(1)}$, $A_0^{(1)*}$ and $A_0^{(1)**}$-surface. These solutions can be expressed by solutions of linear difference equations. Here the $A_0^{(1)}$-surface discrete Painlev\'e equation is the most generic difference equation, as all discrete Painlev\'e equations can be obtained by its degeneration limit. These special solutions exist when the parameters of the discrete Painlev\'e equation satisfy a particular constraint. We consider that these special functions belong to the hypergeometric family although they seems to go beyond the known discrete and $q$-discrete hypergeometric functions. We also discuss the degeneration scheme of these solutions.

Affiliated with

Also associated with

No associations

Rating

Riccati Solutions of Discrete Painlevé Equations with Weyl Group Symmetry of Type $E_8^{(1)}$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Riccati Solutions of Discrete Painlevé Equations with Weyl Group Symmetry of Type $E_8^{(1)}$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Riccati Solutions of Discrete Painlevé Equations with Weyl Group Symmetry of Type $E_8^{(1)}$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-259105