Publication details

Schwarz triangle functions and duality for certain parameters of the generalised Chazy equation

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RANDALL Matthew James

Year of publication 2020
Type Article in Periodical
Magazine / Source New Zealand Journal of Mathematics
MU Faculty or unit

Faculty of Science

Keywords Generalised Chazy equation; Schwarz triangle functions; hypergeometric transformations
Description Schwarz triangle functions play a fundamental role in the solutions of the generalised Chazy equation. We determine the Schwarz triangle func- tions that appear in the solutions in the cases where k = 2 3 , 3 2 , 2 and 3. Chazy has shown that for the parameters k = 2 and 3, the equations can be linearised. Some of the Schwarz triangle functions that show up in the solutions to the generalised Chazy equation with these two parameters also show up in the dual cases where k = 2 3 and k = 3 2 , suggesting an intriguing connection between the solutions for k = 2 and k = 3 with dihedral and tetrahedral symmetry respectively, and the solutions for k = 2 3 ; 3 2 with G2 symmetry. © 2020 New Zealand Mathematical Society and Department of Mathematics, University of Auckland.
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