Experimentations on the Associate Laguerre Basis Set For Certain Univariate Function Matrix Representations

Fluctuation free integration is a promisingly powerful method developed in last decade and it involves the Gauss quadrature as a particular case. The basic idea is to use an approximate matrix representation of the function operator defined via the function to be integrated. Then, this matrix representation is approximated one more time such that the resulting formulae use the matrix representation of the independent variable under consideration as the only matrix entity. Hence the scheme is universal except the function evaluations at the spectral points of the independent variable matrix representation. The basis function set used in the matrix representation is very determinative for the quality of the approximation. This work focuses on the half interval integral utilization in the fluctuation free integration first time and tries to use an associated Laguerre polynomial set. Certain common factors can also be involved in the basis set to give some desired behaviors to the basis functions at the ends of the interval. Some illustrative examples are also presented to show the extent of the method efficieny.