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Conformal Invariants, Inequalities, and Quasiconformal Maps
Basic functions: Hypergeometric Functions Gamma and Beta Functions Complete Elliptic Integrals The Arithmetic-Geometric Mean Quotients of Elliptic Integrals Jacobian Elliptic Functions and Conformal… Expand
Generalized convexity and inequalities
Abstract Let R + = ( 0 , ∞ ) and let M be the family of all mean values of two numbers in R + (some examples are the arithmetic, geometric, and harmonic means). Given m 1 , m 2 ∈ M , we say that a… Expand
Inequalities for quasiconformal mappings in space
A new lower bound for the conformal capacity of the Grotzsch ring and sharp bounds for the radial distortion of a quasiconformal automorphism of the unit ball are obtained in n-space, n > 2
INEQUALITIES FOR ZERO-BALANCED HYPERGEOMETRIC FUNCTIONS
The authors study certain monotoneity and convexity properties of the Gaussian hypergeometric function and those of the Euler gamma function.
A monotonicity property of the gamma function
In this paper we obtain a monotoneity property for the gamma function that yields sharp asymptotic estimates for 17(x) as x tends to oc, thus proving a conjecture about 17(x).
Functional inequalities for hypergeometric functions and complete elliptic integrals
The authors study monotoneity and convexity properties of the Gaussian hypergeometric function, particularly the special cases of complete elliptic integrals. They also prove functional inequalities… Expand
Generalized elliptic integrals and modular equations
In geometric function theory, generalized elliptic integrals and functions arise ?from the Schwarz-Christoffel transformation of the upper half-plane onto a parallelogram and are naturally related to… Expand
Distortion functions for plane quasiconformal mappings
The authors study two well-known distortion functions, λ(K) andϕK(r), of the theory of plane quasiconformal mappings and obtain several new inequalities for them. The proofs make use of some… Expand
Topics in Special Functions III
The authors provide a survey of recent results in special functions of classical analysis and geometric function theory, in particular, the circular and hyperbolic functions, the gamma function, the… Expand