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math.CA2020★ 7 cited
From Heun Class Equations to Painlevé Equations
Jan Dereziński, Artur Ishkhanyan, Adam Latosiński
In the first part of our paper we discuss linear 2nd order differential equations in the complex domain, especially Heun class equations, that is, the Heun equation and its conflue…
math.CA2019★ 6 cited
On the derivatives of the Heun functions
G. Filipuk, A. Ishkhanyan, J. Dereziński
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…
math.CA2019
Group-theoretical origin of symmetries of hypergeometric class equations and functions
Jan Dereziński
We show that properties of hypergeometric class equations and functions become transparent if we derive them from appropriate 2nd order differential equations with constant coeffic…