TY - JOUR
T1 - New error coefficients for estimating quadrature errors for analytic functions
AU - Rabinowitz, Philip
AU - Richter, Nira
PY - 1970/7
Y1 - 1970/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84968510935&partnerID=8YFLogxK
U2 - 10.1090/S0025-5718-1970-0275675-X
DO - 10.1090/S0025-5718-1970-0275675-X
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AN - SCOPUS:84968510935
SN - 0025-5718
VL - 24
SP - 561
EP - 570
JO - Mathematics of Computation
JF - Mathematics of Computation
IS - 111
ER -