Kendall C. Richards

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.

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}

Majorization and domination in the Bergman space

is positive for

Totally monotone functions with applications to the Bergman space

x\in (0,1)

A Note on the Hypergeometric Mean Value

. 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 note on the accuracy of a computable approximation for the period of a pendulum

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

A note on Turán type and mean inequalities for the Kummer function

when

Sharp power mean bounds for the Gaussian hypergeometric function

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

Inequalities for the ratio of complete elliptic integrals

for all positive integers n.