Means in mathematical analysis. Bivariate means )

Content: Front Cover
 Means in Mathematical Analysis
 Copyright
 Contents
 About the Authors
 Preface
 Acknowledgment
 Introduction
 Motivation for this book
 Chapter 1
 Chapter 2
 Chapter 3
 Chapter 4
 1 Classical theory of the AGM
 1.1 Measurement of the circle
 1.2 Heron's method of extracting square roots
 1.3 Lagrange and the de nition of the AGM
 1.4 Lemniscatic integrals
 1.5 Elliptic integrals
 1.6 Hypergeometric series
 1.7 Landen's transformation
 1.8 The perimeter of an ellipse
 2 Means
 2.1 Means and properties of means
 2.1.1 Greek means
 2.1.2 De nition and properties of means 2.1.3 Quasi-arithmetic means2.1.4 Other methods for the construction of means
 2.1.5 Comparison of means
 2.1.6 Weighted means
 2.1.7 Weak and angular inequalities
 2.1.8 Operations with means
 2.1.9 Universal means
 2.1.10 Invariant means
 2.2 Complementariness
 2.2.1 Complementary means
 2.2.2 Algebraic and topological structures on some set of means
 2.2.3 More about pre-means
 2.2.4 Complementary pre-means
 2.2.5 Partial derivatives of pre-means
 2.2.6 Series expansion of means
 2.2.7 Generalized inverses of means
 2.2.8 Complementariness with respect to power means 2.2.9 Complementariness with respect to Lehmer means2.2.10 Complementariness with respect to Gini means
 2.2.11 Complementariness with respect to Stolarsky means
 2.2.12 Complementariness with respect to extended logarithmic means
 2.2.13 Complementariness with respect to the identric mean
 3 Double sequences
 3.1 Archimedean double sequences
 3.2 Determination of A-compound means
 3.3 Rate of convergence of an Archimedean double sequence
 3.4 Acceleration of the convergence
 3.5 Gaussian double sequences
 3.6 Determination of G-compound means 3.7 Rate of convergence of a Gaussian double sequence3.8 Comparison of compound means
 3.9 The Schwab-Borchardt mean
 3.10 Seiffert-like means
 3.11 Double sequences with pre-means
 3.12 Other generalizations of double sequences
 4 Integral means
 4.1 The de nition of the integral mean
 4.2 A recurrence formula
 4.3 Gauss' functional equation
 4.4 Special integral means
 4.5 Comparison of integral means
 4.6 Integral pre-means
 4.7 Special pre-means
 4.8 Estimations of some integral means
 Bibliography
 List of Symbols
 Subject Index
 Author Index
 Back Cover