On a general Maclaurin’s inequality
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- by Stefano Favaro and Stephen G. Walker PDF
- Proc. Amer. Math. Soc. 146 (2018), 175-188 Request permission
Addendum: Proc. Amer. Math. Soc. 146 (2018), 2217-2218.
Abstract:
Maclaurin’s inequality provides a sequence of inequalities that interpolate between the arithmetic mean at the high end and the geometric mean at the low end. We introduce a similar interpolating sequence of inequalities between the weighted arithmetic and geometric mean with arbitrary weights. Maclaurin’s inequality arises for uniform weights. As a by-product we obtain inequalities that may be of interest in the theory of Jacobi polynomials.References
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Additional Information
- Stefano Favaro
- Affiliation: Department of Economics and Statistics, University of Torino, Corso Unione Sovietica 218/bis, 10134 Torino, Italy
- MR Author ID: 855266
- Email: stefano.favaro@unito.it
- Stephen G. Walker
- Affiliation: Department of Mathematics, University of Texas at Austin, One University Station, C1200 Austin, Texas
- MR Author ID: 611731
- Email: s.g.walker@math.utexas.edu
- Received by editor(s): July 11, 2016
- Received by editor(s) in revised form: January 22, 2017
- Published electronically: July 20, 2017
- Communicated by: Mourad E. H. Ismail
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 175-188
- MSC (2010): Primary 26D15, 26C05
- DOI: https://doi.org/10.1090/proc/13673
- MathSciNet review: 3723131