We derive bounds and asymptotics for the maximum Riesz polarization quantity M n(A) := max x1,x2,... ,xn∈A min x∈A n ∑ j=1 1 |x− xj |p (which is n times the Chebyshev constant ) for quite general sets A ⊂ R with special focus on the unit sphere and unit ball. We combine elementary averaging arguments with potential theoretic tools to formulate and prove our results. We also give a discrete vers...

Several authors have examined connections between permutations which avoid 132, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of some of these results for permutations which avoid 1243 and 2143. Using tools developed to prove these analogues, we give enumerations and generating functions for permutations which avoid 1243, 2143, and certain a...

We are concerned with the problem of minimizing the supremum norm on [0, 1] of a nonzero polynomial of degree at most n with integer coefficients. We use the structure of such polynomials to derive an efficient algorithm for computing them. We give a table of these polynomials for degree up to 75 and use a value from this table to answer an open problem due to P. Borwein and T. Erdélyi and impr...

A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials. This is extended to a multi-parameter limit with 3 parameters, also involving (q-)Hahn polynomials, little q-Jacobi polynomials and Jacobi polynomials. Also the limits from Askey–Wilson to Wilson polynomials and from q-Racah to Racah polynomials ar...

In this study, we suggest an efficient and useful method by using Chebyshev polynomials to approximate eigenvalues of a non-singular sixth-order Sturm-Liouville equation. This method uses Chebyshev polynomials and integration operation matrix for approximating of function and its derivatives. We convert the original problem for finding the eigenvalues of Sturm-Liouville problem to a problem of ...

K e y w o r d s B e r n o u l l i polynomials, Euler polynomials, Generating functions, Bernoulli numbers, Euler numbers, Addition theorem, Multiplication theorem~ Generalized Bernoulli polynomials and numbers, Generalized Euler polynomials and numbers. 1. I N T R O D U C T I O N T h e classical Bernoulli polynomials Bn(x) and the classical Euler polynomials En(x) are usual ly def ined by m e a...

It is shown that the zeros of the Faber polynomials generated by a regular m-star are located on the m-star. This proves a recent conjecture of J. Bartolomeo and M. He. The proof uses the connection between zeros of Faber polynomials and Chebyshev quadrature formulas.