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Note on the Schwarz triangle functions

Published online by Cambridge University Press:  17 April 2009

Mark Harmer
Affiliation:
Institute of Information and Mathematical Sciences Massey University Albany, New Zealand, e-mail: m.s.harmer@massey.ac.nz
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We shown the rationality of the Taylor coefficients of the inverse of the Schwarz triangle functions for a triangle group about any vertex of the fundamental domain.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Beardon, A.F., The geometry of discrete groups (Springer-Verlag, Berlin, 1983).CrossRefGoogle Scholar
[2]Harmer, M., Martin, G. and Pavlov, B., ‘Conformal mappings from the upper half plane to fundamental domains on the hyperbolic plane’, (Department of Maths Report series 499, University of Auckland, New Zealand, 2003).Google Scholar
[3]Lehner, J., ‘Note on the Schwarz triangle functions’, Pacific J. Math. 4 (1954), 243249.CrossRefGoogle Scholar
[4]Nehari, Z., Conformal mapping (McGraw-Hill, New York, 1952).Google Scholar