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Department of Mathematics and Computer Science

Department of Mathematics and Computer Science

Recent Submissions

  • Richards, Kendall C. (Proceedings of the American Mathematical Society, 1993)
    Let f and g be functions analytic on the unit disk and let I* denote the Bergman norm. Conditions are identified under which there exists an absolute constant c, with 0 < c < 1, such that the relationship Ig(z)I < ...
  • Richards, Kendall C. (Transactions of the American Mathematical Society, 1993)
    Using a theorem of S. Bernstein [1] we prove a special case of the following maximum principle for the Bergman space conjectured by B. Koren- blum [3]: There exists a number S e (0, 1) such that if / and g are ...
  • Richards, Kendall C. (Mathematics Magazine, 1993)
  • Richards, Kendall C. (Transactions of the American Mathematical Society, 1995)
    The authors study certain monotoneity and convexity properties of the Gaussian hypergeometric function and those of the Euler gamma function.
  • Richards, Kendall C. (Journal of Approximation Theory, 1998)
    Let {φk}n k=0, n<m, be a family of polynomials orthogonal with respect to the positive semi-definite bilinear form (g, h)d := 1 m Xm j=1 g(xj )h(xj ), xj := −1 + (2j − 1)/m. These polynomials are known as Gram ...
  • Richards, Kendall C. (Siam Journal on Mathematical Analysis, 2000)
    In this paper we verify a conjecture of M. Vuorinen that the Muir approxima- tion is a lower approximation to the arc length of an ellipse. Vuorinen conjectured that f(x) = 2F1( 1 2 , − 1 2 ; 1; x) − [(1 + (1 − ...
  • Richards, Kendall C. (Siam Journal on Mathematical Analysis, 2001)
    Conditions are determined under which 3F2 (−n, a, b; a + b + 2, ε − n + 1; 1) is a monotone function of n satisfying ab· 3F2 (−n, a, b; a + b + 2, ε − n + 1; 1) ≥ ab· 2F1 (a, b; a + b + 2; 1) . Motivated by a conjecture ...
  • Richards, Kendall C. (Computational Methods and Function Theory, 2001)
    Recent efforts to obtain bounds for the complete elliptic integral π 2 · 2F1 −1 2 , 1 2 ; 1; r2 in terms of power means and other related means have precipitated the search for similar bounds for the more ...
  • Richards, Kendall C. (Journal of Mathematical Analysis and Applications, 2005)
    Sharp inequalities are established between the Gaussian hypergeometric function and the power mean. These results extend known inequalities involving the complete elliptic integral and the hyper- geometric mean.
  • Richards, Kendall C. (Journal of Inequalities in Pure and Applied Mathematics, 2006)
    Recently obtained inequalities [12] between the Gaussian hypergeometric func- tion and the power mean are applied to establish new sharp inequalities involv- ing the weighted identric, logartithmic, and power means.
  • Richards, Kendall C. (Journal of Inequalities in Pure and Applied Mathematics, 2007)
    In this note, we present sharp inequalities relating hypergeometric analogues of the arithmetic-geometric mean discussed in [5] and the power mean. The main result generalizes the corresponding sharp inequality for the ...
  • Richards, Kendall C. (Journal of Mathematical Analysis and Applications, 2009)
    Turán-type inequalities for combinations of Kummer functions involving Φ(a ± ν, c ± ν, x) and Φ(a, c ± ν, x) have been recently investigated in [Á. Baricz, Functional inequalities involving Bessel and modified Bessel ...
  • Richards, Kendall C. (Journal of Mathematical Inequalities, 2010)
    We give an expository summary of a collection of inequalities involving Gauss’ hyper- geometric function 2F1 and the closely-related power mean (and certain other bivariate means). Two conjectures involving simultaneous ...
  • Richards, Kendall C.; Denman, Richard T.; Futamura, Fumiko (Linear Algebra and Its Applications, 2013)
    It was recently shown that if M = 1 ⊕ ··· ⊕ k ∈ Cn×n is a Jordan matrix with k nontrivial Jordan blocks i, then M can be frame diagonalized by embedding M into a diagonalizable matrix in C(n+)×(n+) with = k. This ...
  • Richards, Kendall C. (The Ramanujan Journal, 2016)
    We develop a collection of single-parameter series representations involving special functions and mathematical constants. The techniques used result in new representations as well as alternative proofs of known representations.
  • Richards, Kendall C. (Aip Advances, 2015)
    We discuss the accuracy of a previously proposed computable approximation for the period of the simple pendulum. In particular, we apply known inequalities for the Gaussian hypergeometric function to prove that the associated ...
  • Richards, Kendall C. (Journal of Mathematical Analysis and Applications, 2015)
    We study monotonicity, concavity and convexity properties of the function Gr(α) = μ(rα) α (0 <r< 1; α > 0), where μ denotes the modulus of the Grötzsch ring. Moreover, we apply our results to obtain various sharp ...
  • Anthony, Barbara M. (Mathematics of Operations Research, 2010)
    This paper studies an extension of the k-median problem under uncertain demand. We are given an n-vertex metric space V d and m client sets Si ⊆ V m i=1. The goal is to open a set of k facilities F such that the ...
  • Anthony, Barbara M. (Consortium for Computing Sciences in Colleges, 2017-12)
    Many computer science courses use final exams as one means of evaluating student performance within the course, but developing meaningful assessments can be both difficult and time-consuming. Students and faculty alike can ...
  • Anthony, Barbara M. (Consortium for Computing Sciences in Colleges, 2014-04)
    An undergraduate computer science colloquium is presented that can enhance the educational opportunities for students at a small liberal arts college while providing an additional community-building venue for majors at ...

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