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Series Solutions of the Non-Stationary Heun Equation
KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics.
KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics.
2018 (English)In: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 14, article id 011Article in journal (Refereed) Published
Abstract [en]

We consider the non-stationary Heun equation, also known as quantum Painleve 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.

Place, publisher, year, edition, pages
NATL ACAD SCI UKRAINE, INST MATH , 2018. Vol. 14, article id 011
Keywords [en]
Heun equation, Lame equation, Kernel functions, quantum Painleve VI, perturbation theory
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-224070DOI: 10.3842/SIGMA.2018.011ISI: 000425364200001Scopus ID: 2-s2.0-85045072982OAI: oai:DiVA.org:kth-224070DiVA, id: diva2:1190497
Note

QC 20180314

Available from: 2018-03-14 Created: 2018-03-14 Last updated: 2018-03-14Bibliographically approved

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Langmann, Edwin

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