Abstract:
The confluent Heun equation and confluent hypergeometric equation are studied in scalar and vector forms with particular emphasis to the role of apparent singularities. The relation to the Painlevé equation is shown.
Key words and phrases:
confluent hypergeometric equation, confluent Heun equation, deformed Heun equation, integral symmetries, antiquantization, Painlevé equation.
Citation:
S. Yu. Slavyanov, A. A. Salatich, “Confluent Heun equation and confluent hypergeometric equation”, Representation theory, dynamical systems, combinatorial methods. Part XXVIII, Zap. Nauchn. Sem. POMI, 462, POMI, St. Petersburg, 2017, 93–102; J. Math. Sci. (N. Y.), 232:2 (2018), 157–163
This publication is cited in the following 3 articles:
Maria Korovina, Ilya Smirnov, “Method for Investigation of Convergence of Formal Series Involved in Asymptotics of Solutions of Second-Order Differential Equations in the Neighborhood of Irregular Singular Points”, Axioms, 13:12 (2024), 853
A. A. Salatich, S.Yu. Slavyanov, O. L. Stesik, “First-Order Ode Systems Generating Confluent Heun Equations”, J Math Sci, 251:3 (2020), 427
T A Ishkhanyan, V P Krainov, A M Ishkhanyan, “Confluent hypergeometric expansions of the confluent Heun function governed by two-term recurrence relations”, J. Phys.: Conf. Ser., 1416:1 (2019), 012014