New error coefficients for estimating quadrature errors for analytic functions

Philip Rabinowitz*, Nira Richter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

Since properly normalized Chebyshev polynomials of the first kind T(z) satisfy f,(z)71 - z2dz\ = Smn for ellipses ep with foci at 1, any function analytic in ep has an expansion,/(z) = J3 anfn{z) with a„ = (/, Tn). Applying the integration error operator E yields E(J) = 2˜Z a„E(Tn)- Applying the Cauchy-Schwarz inequality to E(J) leads to the inequality.

Original languageEnglish
Pages (from-to)561-570
Number of pages10
JournalMathematics of Computation
Volume24
Issue number111
DOIs
StatePublished - Jul 1970
Externally publishedYes

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