During the presentation, I will discuss a new approach to hypergeometric
class equations. Instead of analyzing each equation separately, we can
examine the general concept of Miller's Lie algebra and construct a
family of differential operators. By studying the algebraic properties
of these operators, we can derive properties for the entire family of
equations.
This approach provides a unified framework for understanding and
deriving the properties of hypergeometric class equations. In the second
part of the presentation, I will present some examples that illustrate
this approach.
The presentation is based on an unpublished paper by Professor Jan
Dereziński.