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

Abstract

We study Heun's differential equation in the case that one of the singularities is apparent. In particular we conjecture a relationship with generalized hypergeometric differential equation and establish it in some cases. We apply our results to exceptional Jacobi polynomials.

15 pages; validity of the conjecture was extended

References in corpus (1)

• Infinitely many shape invariant potentials and new orthogonal polynomials

Cited by in corpus (14)

• Exceptional Jacobi polynomials
• Potentials of the Heun class
• Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions
• Expansions of the solutions of the general Heun equation governed by two-term recurrence relations for coefficients
• Generalized hypergeometric solutions of the Heun equation
• 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 confluent hypergeometric solutions of the Heun confluent equation
• Confluent hypergeometric expansions of the confluent Heun function governed by two-term recurrence relations
• Confluence of apparent singularities in multi-indexed orthogonal polynomials: the Jacobi case
• A note on the generalized-hypergeometric solutions of general and single-confluent Heun equations
• Generalized Rayleigh and Jacobi processes and exceptional orthogonal polynomials
• Physical Problems Admitting Heun-to-Hypergeometric Reduction
• On the Liouvillian solutions to the perturbation equations of the Schwarzschild black hole