On the solution of the finite moment problem (Q1206966)

Let us consider the following first-kind integral equation with discrete data (1) \(Af=m\), \((Af)_ i:=\int_{-1}^ 1 x^{i-1} f(x)dx\), \(i=1,\dots,n\), where \(m:=(m_ 1,\dots,m_ n)\) is the known vector of moments and \(f\) is an unknown function. The authors give a method to obtain the normal solution of the equation (1) by a linear combination of Jacobi polynomials and obtain its coefficients in terms of the moments. Using ``MATLAB-386 Version 3.5e'' the authors show a number of examples to illustrate the method.