Special functions as solutions to discrete Painlevé equations

  • Authors:

  • K. M. Tamizhmani;A. Ramani;T. Tamizhmani;B. Grammaticos

  • Affiliations:

  • Department of Mathematics, Pondicherry University, Kalapet, Pondicherry 605014, India;CPT, Ecole Polytechnique, CNRS, UMR 7644, Palaiseau 91128, France;GMPIB, Université Paris VII, Tour 24-14, 5e étage, case 7021, Paris 75251, France and Department of Mathematics, Avvaiyar Government College for Women, Karaikal, India;GMPIB, Université Paris VII, Tour 24-14, 5e étage, case 7021, Paris 75251, France

  • Venue:
  • Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on special functions and their applications
  • Year:
  • 2003

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Abstract

We present results on special solutions of discrete Painlevé equations. These solutions exist only when one constraint among the parameters of the equation is satisfied and are obtained through the solutions of linear second-order (discrete) equations. These linear equations define the discrete analogues of special functions.