Abstract
The classical Poincaré-Bertrand transposition formula for the inversion of the order of integration in repeated Cauchy-type integrals is generalized in accordance with a new interpretation of Cauchy-type integrals. Next, the Gauss-Jacobi quadrature rule is applied, in a particular case of the generalized Poincaré-Bertrand formula, to both members of this formula and it is proved that this formula still remains valid (after the approximation of the integrals by quadrature sums). Two simple applications of this result, one concerning the convergence of a quadrature rule for repeated Cauchy-type integrals, and the other the numerical solution of singular integral equations, are made. Further generalizations and applications of the present results follow easily.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
