We apply Zeilberger’s algorithm to generate relations of finite-type necessary to obtain inner bounds for the extreme zeros of orthogonal polynomial sequences with 3F2 hypergeometric representations. Using this method, we improve previously obtained upper bounds for the smallest and lower bounds for the largest zeros of the Hahn polynomials and we identify inner bounds for the extreme zeros of ...

Beatrice Hahn, elected to the National Academy of Sciences in 2012, has a longstanding interest in the origins and evolution of human pathogens. She is recognized for deciphering the primate origins of human immunodeficiency viruses types 1 and 2 (HIV-1 and HIV-2) and the malaria parasite Plasmodium falciparum. Hahn has also developed noninvasive methods to study the zoonotic potential of micro...

Orthogonal moments are recognized as useful tools for object representation and image analysis. It has been shown that the recently developed discrete orthogonal moments have better performance than the conventional continuous orthogonal moments. In this paper, a new set of discrete orthogonal polynomials, namely Hahn polynomials, are introduced. The related Hahn moment functions defined on thi...

We work in the set theory without the axiom of choice: ZF. Though the Hahn-Banach theorem cannot be proved in ZF, we prove that every Gâteauxdifferentiable uniformly convex Banach space E satisfies the following continuous Hahn-Banach property: if p is a continuous sublinear functional on E, if F is a subspace of E, and if f : F → R is a linear functional such that f ≤ p|F , then there exists a...

As a cornerstone of functional analysis, Hahn–Banach theorem constitutes an indispensable tool of modern analysis where its impact extends beyond the frontiers of linear functional analysis into several other domains of mathematics, including complex analysis, partial differential equations and ergodic theory besides many more. The paper is an attempt to draw attention to certain applications o...

ð2Þ ~ T 1⁄4 T ; 8 2 V: We use HBðV;W Þ to denote the set of Hahn–Banach operators. The classical Hahn–Banach theorem states that every rank-1 operator from V into W is a Hahn–Banach operator. It can also be restated in the following way: if dimW 1⁄4 1, then HBðV;W Þ 1⁄4 LðV;W Þ. Observe that the two statements above are slightly different. In the first case we describe a property of an operator...

We consider the unital associative algebra A with two generators X, Z obeying defining relation [Z,X]=Z2+Δ. construct irreducible tridiagonal representations of A. Depending on value parameter Δ, these are associated to Jacobi matrices para-Krawtchouk, continuous Hahn, Hahn or polynomials.