New Error Coefficients for Estimating Quadrature Errors for Analytic Functions
New Error Coefficients for Estimating Quadrature Errors for Analytic Functions
Since properly normalized Chebyshev polynomials of the first kind ${\tilde T_n}(Z)$ satisfy \[ ({\tilde T_m},{\tilde T_n}) = \int _{ \in \rho } {{{\tilde T}_m}({\text {z}})} \overline {{T_n}({\text {z}})} |1 - {{\text {z}}^2}{|^{ - 1/2}}|d{\text {z}}| = {\delta _{mn}}\] for ellipses $\in \rho$ with foci at $\pm 1$, any function analytic …