• 用于逼近下列类型的积分值:

                                          

where xi is the i-th root of Laguerre polynomial Ln(x) and the weight wi is given by

It fits all polynomials of degree 2m-1 exactly (Chandrasekhar 1960, p. 61).

  • 为了求得more general函数f(x)的积分,一般会用下面的transformation:

                                  

Note, that while this approach works from an analytical perspective, it is not always numerically stable.(注意:有时候这种方法求出的结果不准确!!)

  • Generalized Gauss–Laguerre quadrature

                   

学习链接:https://mathworld.wolfram.com/Laguerre-GaussQuadrature.html

https://www.mathworks.com/matlabcentral/fileexchange/8067-gauss-laguerre

https://people.sc.fsu.edu/~jburkardt/m_src/gen_laguerre_rule/gen_laguerre_rule.html

维基百科:file:///C:/Users/marui-2607/Desktop/Gauss%E2%80%93Laguerre%20quadrature%20-%20Wikipedia.mhtml

百度文库:https://wenku.baidu.com/view/17a4574a02d8ce2f0066f5335a8102d276a26124.html?rec_flag=default&word=Gauss%E2%80%93Laguerre%20quadrature&fr=pc_oldview_relate-1001_1-5-wk_rec_doc2-1001_1-57270722192e45361066f505-17a4574a02d8ce2f0066f5335a8102d276a26124

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