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Publications Influence

Conformal Invariants, Inequalities, and Quasiconformal Maps

- G. Anderson, M. Vamanamurthy, M. Vuorinen
- Mathematics
- 1 July 1997

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

422 17

Generalized convexity and inequalities

- G. Anderson, M. Vamanamurthy, M. Vuorinen
- Mathematics
- 9 January 2007

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

152 10- PDF

Inequalities for quasiconformal mappings in space

- G. Anderson, M. Vamanamurthy, M. Vuorinen
- Mathematics
- 1 September 1993

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

114 6- PDF

INEQUALITIES FOR ZERO-BALANCED HYPERGEOMETRIC FUNCTIONS

- G. Anderson, R. Barnard, K. C. Richards, M. Vamanamurthy, M. Vuorinen
- Mathematics
- 1 May 1995

The authors study certain monotoneity and convexity properties of the Gaussian hypergeometric function and those of the Euler gamma function.

127 6- PDF

A monotonicity property of the gamma function

- G. Anderson, S. Qiu
- Mathematics
- 1997

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).

93 5- PDF

Functional inequalities for hypergeometric functions and complete elliptic integrals

- G. Anderson, M. Vamanamurthy, M. Vuorinen
- Mathematics
- 1 March 1992

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

79 4

Generalized elliptic integrals and modular equations

- G. Anderson, S. Qiu, M. Vamanamurthy, M. Vuorinen
- Mathematics
- 2000

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

199 3- PDF

Functions of several complex variables

- W. Kaplan, G. Anderson
- Mathematics
- 1964

25 2- PDF

Distortion functions for plane quasiconformal mappings

- G. Anderson, M. Vamanamurthy, M. Vuorinen
- Mathematics
- 1 February 1988

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

46 2

Topics in Special Functions III

- G. Anderson, M. Vuorinen, Xiaohui Zhang
- Mathematics
- 17 January 2007

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

38 1- PDF

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