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On one-parameter family of bivariate means. (English) Zbl 1238.33011
A one-parameter family of bivariate means is introduced. They are defined in terms of the inverse functions of Jacobian elliptic functions $cn$ and $nc$, formulas 2.5 and 2.6. It is shown that the new means are symmetric and homogeneous of degree one in their variables. Members of this family of means interpolate an inequality which connects two Schwab-Borchardt means. Computable lower and upper bounds for the new mean are also established. Reviewer’s remark: The formulas 2.5 and 2.6. are not the same as in [p. 596] [{\it M. Abramowitz} (ed.) and {\it I. A. Stegun} (ed.), Handbook of mathematical functions with formulas, graphs, and mathematical tables. Reprint of the 1972 ed.. John Wiley & Sons, Inc; Washington, D.C.: National Bureau of Standard, (1984; Zbl 0643.33001)] . The $u$ should be changed to $x$ in both formulas.

33E05Elliptic functions and integrals
26D07Inequalities involving other types of real functions
Full Text: DOI
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