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Quadrature formulas of Birkhoff type ((0,3) and (0,4) cases) which are exact for all algebraic polynomials of degree at most 2n-1 is developed. The nodes of such quadrature are taken in the zeros of the polynomial where Pn
is the Legendre polynomial of degree n. The corresponding quadrature formulas based on the zeros of (1,2) still remain open.
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