On the derivatives of the Heun functions

Abstract

The Heun functions satisfy linear ordinary differential equations of second order with certain singularities in the complex plane. The first order derivatives of the Heun functions satisfy linear second order differential equations with one more singularity. In this paper we compare these equations with linear differential equations isomonodromy deformations of which are described by the Painlevé equations $P_{II}-P_{VI}$.

References in corpus (5)

• The 192 Solutions of the Heun Equation
• A Quantum Space Behind Simple Quantum Mechanics
• New solutions of Heun general equation
• Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions
• Parametric transformations between the Heun and Gauss hypergeometric functions

Cited by in corpus (2)

• From Heun Class Equations to Painlevé Equations
• Recurrence relations and general solution of the exceptional Hermite equation