Heun's equation, generalized hypergeometric function and exceptional Jacobi polynomial

DOI10.1088/1751-8113/45/8/085211zbMath1247.34132arXiv1106.1543OpenAlexW3104887965MaRDI QIDQ3225309

Kouichi Takemura

Publication date: 19 March 2012

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.1543

zbMATH Keywords

hypergeometric functionHeun's equationexceptional Jacobi polynomial

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Lamé, Mathieu, and spheroidal wave functions (33E10)

Related Items (14)

Expansions of the solutions of the general Heun equation governed by two-term recurrence relations for coefficients ⋮ Extensions of a class of similarity solutions of Fokker-Planck equation with time-dependent coefficients and fixed/moving boundaries ⋮ A note on the generalized-hypergeometric solutions of general and single-confluent Heun equations ⋮ On the Liouvillian solutions to the perturbation equations of the Schwarzschild black hole ⋮ Generalized hypergeometric solutions of the Heun equation ⋮ Exceptional Jacobi polynomials ⋮ About families of orthogonal polynomials satisfying Heun's differential equation ⋮ Resolving singularities and monodromy reduction of Fuchsian connections ⋮ Non-commutativity and non-inertial effects on the Dirac oscillator in a cosmic string space-time ⋮ Generalized-hypergeometric solutions of the general Fuchsian linear ODE having five regular singularities ⋮ Generalized-hypergeometric solutions of the biconfluent Heun equation ⋮ Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions ⋮ Generalized confluent hypergeometric solutions of the Heun confluent equation ⋮ GENERALIZED RAYLEIGH AND JACOBI PROCESSES AND EXCEPTIONAL ORTHOGONAL POLYNOMIALS

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