RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



SIGMA:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


SIGMA, 2018, Volume 14, 011, 32 pages (Mi sigma1310)  

Series Solutions of the Non-Stationary Heun Equation

Farrokh Ataiab, Edwin Langmannb

a Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan
b Department of Physics, KTH Royal Institute of Technology, SE-10691 Stockholm, Sweden

Abstract: We consider the non-stationary Heun equation, also known as quantum Painlevé VI, which has appeared in different works on quantum integrable models and conformal field theory. We use a generalized kernel function identity to transform the problem to solve this equation into a differential-difference equation which, as we show, can be solved by efficient recursive algorithms. We thus obtain series representations of solutions which provide elliptic generalizations of the Jacobi polynomials. These series reproduce, in a limiting case, a perturbative solution of the Heun equation due to Takemura, but our method is different in that we expand in non-conventional basis functions that allow us to obtain explicit formulas to all orders; in particular, for special parameter values, our series reduce to a single term.

Keywords: Heun equation; Lamé equation; Kernel functions; quantum Painlevé VI; perturbation theory.

Funding Agency Grant Number
Stiftelsen Olle Engkvist Byggmästare 184-0573
We gratefully acknowledge partial financial support by the Stiftelse Olle Engkvist Byggmästare (contract 184-0573).


DOI: https://doi.org/10.3842/SIGMA.2018.011

Full text: PDF file (623 kB)
Full text: http://www.emis.de/.../011
References: PDF file   HTML file

Bibliographic databases:

MSC: 33E20; 81Q05; 16R60
Received: October 10, 2017; in final form February 8, 2018; Published online February 16, 2018
Language:

Citation: Farrokh Atai, Edwin Langmann, “Series Solutions of the Non-Stationary Heun Equation”, SIGMA, 14 (2018), 011, 32 pp.

Citation in format AMSBIB
\Bibitem{AtaLan18}
\by Farrokh~Atai, Edwin~Langmann
\paper Series Solutions of the Non-Stationary Heun Equation
\jour SIGMA
\yr 2018
\vol 14
\papernumber 011
\totalpages 32
\mathnet{http://mi.mathnet.ru/sigma1310}
\crossref{https://doi.org/10.3842/SIGMA.2018.011}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000425364200001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85045072982}


Linking options:
  • http://mi.mathnet.ru/eng/sigma1310
  • http://mi.mathnet.ru/eng/sigma/v14/p11

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Symmetry, Integrability and Geometry: Methods and Applications
    Number of views:
    This page:95
    Full text:21
    References:16

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020