engleski

General Two-point Quadrature Formulae

General two-point integral quadrature formulae are considered. For deriving those formulae the sequences of harmonic polynomials and $w-$harmonic functions are used. Some best possible and sharp error estimates are obtained for the functions whose higher order derivatives belong to L_p[a, b] spaces. Classical trapezoidal, midpoint, open type Newton-Cotes two-point formula and Maclaurin two- point formula are obtained as special cases of the first formula. Weighted two-point quadrature formula is produced as the special case of the $m- $point formula. Special types of the weighted functions are used in establishing the generalizations of the Gauss-Legendre, Gauss- Chebyshev and Gauss-Hermite formulae.

quadrature formula; two-point formula; trapezoid; Newton-Cotes; midpoint; Maclaurin; weighted formula; Gaussian form

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