Weighted quadrature rules with weight function x-pe-1x on [0, ∞)

摘要

In this paper, we introduce an analytical class of weighted quadrature rules whose weight function is as W(x,p)=x-pe-1x on [0, ∞).The formulas given in this work generally obey the following form:∫0∞x-pe-1xf(x)dx=∑i=1nwif(xi)+Rn[f],in which xi are the zeros of polynomials orthogonal with respect to the introduced weight function, wi are the corresponding coefficients and Rn[f] is the related error. It should be pointed out that the above formula is valid only for the finite values of n. In other words, the condition p > 2{max n} + 1 is essential in order to be applicable the above quadrature rule. Some analytical examples are finally given and compared.