Hypergeometric Functions and Their Generalizations to Higher Dimensions: A study of the classical hypergeometric function and its generalizations associated with root systems
Typ
Examensarbete för masterexamen
Master's Thesis
Master's Thesis
Program
Engineering mathematics and computational science (MPENM), MSc
Publicerad
2024
Författare
Johansson, Oskar
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
The hypergeometric differential equation is a classical ODE of second order, and it
was already studied by Gauss. The hypergeometric function is classically defined as
the solution to this equation that is analytic at x = 0. With this definition it is not
obvious how to generalize the hypergeometric function to higher dimensions. With
a shift in perspective we can arrive at the same differential equation by studying a
certain eigenvalue problem of polynomials of so called Dunkl operators. These are
easier to generalize and will lead us to hypergeometric functions associated with so
called root systems in higher dimension.
Beskrivning
Ämne/nyckelord
Hypergeometric differential equation, Hypergeometric function, Root system, Dunkl operators.