In classical theorems on the convergence of Gaussian quadrature formulas for power orthogonal polynomials with respect to a weight w on I （a,b）, a function G E S（w）= （f： fxlf（x）lw（x）dx 〈 ∞ satisfying the ...In classical theorems on the convergence of Gaussian quadrature formulas for power orthogonal polynomials with respect to a weight w on I （a,b）, a function G E S（w）= （f： fxlf（x）lw（x）dx 〈 ∞ satisfying the conditions G（2J）（x） ：〉 O, x E （a,b）, j = 0, 1 , and growing as fast as possible as x→ a- and x → b-, plays an important role. But to find such a function G is often difficult and complicated. This implies that to prove convergence of Gaussian quadrature formulas, it is enough to find a function G E S（w） with G ≥ 0 satisfying展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 11171100,10871065,11071064)the Hunan Provincial Natural Science Foundation of China (No. 10JJ3089)the Scientific Research Fund of Hunan Provincial Education Department (No. 11W012)
文摘In classical theorems on the convergence of Gaussian quadrature formulas for power orthogonal polynomials with respect to a weight w on I （a,b）, a function G E S（w）= （f： fxlf（x）lw（x）dx 〈 ∞ satisfying the conditions G（2J）（x） ：〉 O, x E （a,b）, j = 0, 1 , and growing as fast as possible as x→ a- and x → b-, plays an important role. But to find such a function G is often difficult and complicated. This implies that to prove convergence of Gaussian quadrature formulas, it is enough to find a function G E S（w） with G ≥ 0 satisfying
