A discrete integral representation for polynomials of fixed maximal degree and their universal Korovkin closure.
The paper gives such an iterative method for special Chebyshev approxiamtions that its order of convergence is . Somewhat comparable results are found in [1] and [2], based on another idea.
An infinite series which arises in certain applications of the Lagrange-Bürmann formula to exponential functions is investigated. Several very exact estimates for the Laplace transform and higher moments of this function are developed.
We obtain, for entire functions of exponential type satisfying certain integrability conditions, a quadrature formula using the zeros of spherical Bessel functions as nodes. We deduce from this quadrature formula a result of Olivier and Rahman, which refines itself a formula of Boas.