We construct a set of polynomials φ n ( x ,ζ) which are orthogonal with respect to w ( x )/( x − ζ) 2 , where w x is a weight function. These polynomials can be used for the definition of a Gauss quadrature formula for the finite part integral magnified image The process is exactly the same as the one used for the extraction of the classical Gauss formula for the Riemann integrals. Three different methods are derived. The first and most accurate quadrature formula is successfully tested in some numerical examples. The proposed quadrature formulas have many applications in problems of mathematical physics, mechanics, etc.
No takes yet. Share an insight, caveat, or question.
Tsamasphyros et al. (1990) studied this question.
Synapse has enriched 5 related papers. Consider them for comparative context: