67
Views
0
CrossRef citations to date
0
Altmetric
Articles

Unique special solution for discrete Painlevé II

Pages 465-474 | Received 23 Aug 2023, Accepted 08 Dec 2023, Published online: 27 Dec 2023

References

  • S.M. Alsulami, P. Nevai, J. Szabados, and W. Van Assche, A family of nonlinear difference equations: Existence, uniqueness, and asymptotic behavior of positive solutions, J. Approx. Theory. 193 (2015), pp. 39–55.
  • P.A. Clarkson, A.F. Loureiro, and W. Van Assche, Unique positive solution for an alternative discrete Painlevé I equation, J. Difference Equ. Appl. 22 (2016), pp. 656–675.
  • M. Duits and D. Holcomb, A double scaling limit for the d-PII equation with boundary conditions. arXiv:2304.02918 [math.CA].
  • M.E.H. Ismail, Classical and Quantum Orthogonal Polynomials in One Variable, Encyclopedia of Mathematics and its Applications Vol. 98, Cambridge University Press, 2005.
  • K. Kajiwara, M. Noumi, and Y. Yamada, Geometric aspects of Painlevé equations, J. Phys. A: Math. Theor. 50 (2017), Aricle ID 073001, 164 pp.
  • T. Lasic Latimer, Unique positive solutions to q-discrete equations associated with orthogonal polynomials, J. Difference Equ. Appl. 27 (2021), pp. 763–775.
  • J.S. Lew and D.A. Quarles, Nonnegative solutions of a nonlinear recurrence, J. Approx. Theory 38 (1983), pp. 357–379.
  • P. Nevai, Orthogonal polynomials associated with exp⁡(−x4), in Second Edmonton Conference on Approximation Theory, CMS Conference Proceedings, Vol. 3, Z. Ditzian, A. Meir, S. D. Riemenschneider and A. Sharma, eds., American Mathematical Society, Providence, RI, 1983, pp. 263–285.
  • F.W.J. Olver, D.W. Lozier, R.F. Boisvert, and C.W. Clark, The NIST Handbook of Mathematical Functions, Cambridge University Press, 2010.
  • F.W.J. Olver, A.B. Olde Daalhuis, D.W. Lozier, B.I. Schneider, R.F. Boisvert, C.W. Clark, B.R. Miller, B.V. Saunders, H.S. Cohl, and M.A. McClain (eds.), NIST Digital Library of Mathematical Functions, Available at https://dlmf.nist.gov/, Release 1.1.10 of 2023-06-15.
  • V. Periwal and D. Shevitz, Unitary-matrix models as exactly solvable string theories, Phys. Rev. Lett. 64 (1990), pp. 1326–1329.
  • A. Ramani, B. Grammaticos, T. Tamizhmani, and K.M. Tamizhmani, Special function solutions of the discrete Painlevé equations, Comput. Math. Appl. 42 (2001), pp. 603–614.
  • B. Simon, Orthogonal Polynomials on the Unit Circle, Amer. Math. Soc. Colloq. Publ. Vol. 54, Part 1 and Part 2, Amer. Math. Soc., Providence, RI, 2005.
  • G. Szegő, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ. Vol. 23, 4th ed. 1975, Amer. Math. Soc., Providence, RI, 1939.
  • W. Van Assche, Orthogonal Polynomials and Painlevé Equations, Australian Mathematical Society Lecture Series, Vol. 27, Cambridge University Press, Cambridge, 2018.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.