The paper claims an optimal endpoint-corrected trapezoidal rule in the Sobolev space W_2^{(2,1)} with an O(h^4) error, but the proof of the error formula is algebraically inconsistent.
K¨ ohler, On the weights of Sard’s quadrature formulas, Calcolo, 25 (1988) 169–186
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The order of convergence of an optimal quadrature formula with derivative in the space $W_2^{(2,1)}$
The paper claims an optimal endpoint-corrected trapezoidal rule in the Sobolev space W_2^{(2,1)} with an O(h^4) error, but the proof of the error formula is algebraically inconsistent.