Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Application of quadrature rules for Cauchy-type integrals to the generalized Poincaré-Bertrand formula

Author: N. I. Ioakimidis
Journal: Math. Comp. 44 (1985), 199-206
MSC: Primary 65D32; Secondary 65R20
MathSciNet review: 771041
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D32, 65R20

Retrieve articles in all journals with MSC: 65D32, 65R20

Additional Information

Article copyright: © Copyright 1985 American Mathematical Society