Computational Methods and Function Theory 9 (2009), No. 1, 269--284
Copyright Heldermann Verlag 2009
Glen D. Anderson
anderson@math.msu.edu , Michigan State University, Department of Mathematics, East Lansing, MI 48824, U.S.A.
Toshiyuki Sugawa
sugawa@math.is.tohoku.ac.jp , Tohoku University, Graduate School of Information Sciences, Sendai 980-8579, Japan.
Mavina K. Vamanamurthy
vamanamu@math.auckland.ac.nz , University of Auckland, Department of Mathematics, Auckland, New Zealand.
Matti Vuorinen
vuorinen@utu.fi , University of Turku, Department of Mathematics, Vesilinnantie 5, FIN-20014, Finland.
We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.
Keywords: Hypergeometric functions, complete elliptic integrals, convexity, hyperbolic metric, Poincaré density.
MSC 2000: Primary 30F45; Secondary 33C05, 33C75, 33E05.
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