DEGREE OF POLYNOMIAL APPROXIMATION TO AN ANALYTIC FUNCTION AS MEASURED BY A SURFACE INTEGRAL

NOTE ON DEGREE OF TRIGONOMETRIC AND POLYNOMIAL APPROXIMATION TO AN ANALYTIC FUNCTION, IN THE SENSE OF LEAST pTK POWERS

A method to obtain the best uniform polynomial approximation for the family of rational function

In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

Note on Degree of Trigonometric and Polynomial Approximation to an Analytic Function § J. L. Walsh and W. E. Sewell

/ d e i \ (is) y — r*?W' = -/"Y'. \dx* c h / The factor — r on the right-hand side of this equation shows that the Dirac equation for an electron is not invariant under inversions. However, if we set 0? = O and JU = 0, then equation (15) is numerically invariant under inversions. This is done in the neutrino theory of light. Hence that theory has the same invariance properties as the Maxwell th...

On the Degree of Polynomial Approximation to Harmonic and Analytic Functions

Degree of Approximation to a Continuous Function on a Non-analytic Curve.

* This research was supported in part by the United States Air Force under contract No. AF49(638)42, monitored by the Air Force Office of Scientific Research of the Air Research and Development Command; and in part by the National Science Foundation. 1 For basic concepts pertaining to categories and functors, cf. Eilenberg, S., and N. Steenrod, Foundations of Algebraic Topology (Princeton Unive...