In their study of a quartic integral, Boros and Moll discovered a special class of Jacobi polynomials, which we call the Boros-Moll polynomials. Kauers and Paule proved the conjecture of Moll that these polynomials are logconcave. In this paper, we show that the Boros-Moll polynomials possess the ratio monotone property which implies the log-concavity and the spiral property. We conclude with a...

The problem is the ordinary differential equation du/dt = -p exp( -q/u) with u(O) = u. We prove that the general three-parameter problem may be reduced through a group invariance to computing a single, parameter-free function w(f). This solution may be most compactly expressed in the form w = l/ln(t*ti(t*)B(r)), where 7 = ln(ln(t*)) and t* = t + exp(1). We compute a Chebyshev series for B(7) fo...

The mth Chebyshev polynomial of a square matrix A is the monic polynomial that minimizes the matrix 2-norm of p(A) over all monic polynomials p(z) of degree m. This polynomial is uniquely defined if m is less than the degree of the minimal polynomial of A. We study general properties of Chebyshev polynomials of matrices, which in some cases turn out to be generalizations of well known propertie...

In the present paper polynomial interpolating scaling function and wavelets are constructed by using the interpolation properties of de la Vallée Poussin kernels with respect to the four kinds of Chebyshev weights. For the decomposition and reconstruction of a given function efficient algorithms based on fast discrete cosine and sine transforms are proposed.

In this paper we discuss a method to design 2 dimensional (2D) FIR filters with the help of Chebyshev polynomials. The polynomial is first converted into a 2D function and later a mapping function is used to design the filters. By the proposed technique one can design filters with various types of passband.

The theoretical and computational aspects of interval methodology based on Chebyshev polynomials for modeling complex nonlinear multi-body dynamic systems in the presence of parametric and external excitation uncertainties is formulated, implemented, and validated. Both the parameters uncertainties and external excitation uncertainties are modeled by uncertain-butbounded interval variables, whe...

In this paper we study the growth rates of Artin monoids and we show that 4 is a universal upper bound. We also show that the generating functions of the associated right-angled Artin monoids are given by families of Chebyshev polynomials. Applications to Artin groups and positive braids are given.

Chebfun is an established software system for computing with functions of a real variable, but its capabilities for handling functions with singularities are limited. Here an analogous system is described based on sinc function expansions instead of Chebyshev series. This experiment sheds light on the strengths and weaknesses of sinc function techniques. It also serves as a review of some of th...

We investigate a family of distributions having a property of stability-underaddition, provided that the number ν of added-up random variables in the random sum is also a random variable. We call the corresponding property a ν-stability and investigate the situation with the semigroup generated by the generating function of ν is commutative. Using results from the theory of iterations of analyt...

in this note, we characterize chebyshev subalgebras of unital jb-algebras. we exhibit that if b is chebyshev subalgebra of a unital jb-algebra a, then either b is a trivial subalgebra of a or a= h r .l, where h is a hilbert space