Kent Pearce

An inequality involving the generalized hypergeometric function and the arc length of an ellipse

In this paper we verify a conjecture of M. Vuorinen that the Muir approximation is a lower approximation to the arc length of an ellipse. Vuorinen conjectured that

A Monotonicity Property Involving 3F2 and Comparisons of the Classical Approximations of Elliptical Arc Length

f(x)={}_{2}F_{1}({\frac{1}{2}},-{\frac{1}{2}};1;x)-[(1+(1-x)^{3/4})/2]^{2/3}

Rounding corners of gearlike domains and the omitted area problem

is positive for

Polynomials with nonnegative coefficients

x\in (0,1)

On a Coefficient Conjecture of Brannan

. The authors prove a much stronger result which says that the Maclaurin coefficients of f are nonnegative. As a key lemma, we show that

A Constructive Method for Numerically Computing Conformal Mappings for Gearlike Domains

{}_{3}F_{2}(-n,a,b;1+a+b,1+\epsilon -n;1) > 0

Parameter identification by continuation methods

when

Numerical solution of positive sum exponential equations

0 < ab/(1+a+b) < \epsilon < 1

A variational method for hyperbolically convex functions

for all positive integers n.

Three Extremal Problems for Hyperbolically Convex Functions

Conditions are determined under which