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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Application of quadrature rules for Cauchy-type integrals to the generalized Poincaré-Bertrand formula
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by N. I. Ioakimidis PDF
Math. Comp. 44 (1985), 199-206 Request permission

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.
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Math. Comp. 44 (1985), 199-206
  • MSC: Primary 65D32; Secondary 65R20
  • DOI: https://doi.org/10.1090/S0025-5718-1985-0771041-X
  • MathSciNet review: 771041