## Hypergeometric Functions and Their Generalizations to Higher Dimensions: A study of the classical hypergeometric function and its generalizations associated with root systems

 dc.contributor.author Johansson, Oskar dc.contributor.department Chalmers tekniska hÃ¶gskola / Institutionen fÃ¶r matematiska vetenskaper sv dc.contributor.examiner HallnÃ¤s, Martin dc.contributor.supervisor HallnÃ¤s, Martin dc.date.accessioned 2024-06-20T11:28:10Z dc.date.available 2024-06-20T11:28:10Z dc.date.issued 2024 dc.date.submitted dc.description.abstract 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. dc.identifier.coursecode MVEX03 dc.identifier.uri http://hdl.handle.net/20.500.12380/307967 dc.language.iso eng dc.setspec.uppsok PhysicsChemistryMaths dc.subject Hypergeometric differential equation, Hypergeometric function, Root system, Dunkl operators. dc.title Hypergeometric Functions and Their Generalizations to Higher Dimensions: A study of the classical hypergeometric function and its generalizations associated with root systems dc.type.degree Examensarbete fÃ¶r masterexamen sv dc.type.degree Master's Thesis en dc.type.uppsok H local.programme Engineering mathematics and computational science (MPENM), MSc
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