# 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

## Noninterpolatory integration rules for Cauchy principal value integralsHTML articles powered by AMS MathViewer

by P. Rabinowitz and D. S. Lubinsky
Math. Comp. 53 (1989), 279-295 Request permission

## Abstract:

Let $w(x)$ be an admissible weight on $[ - 1,1]$ and let $\{ {p_n}(x)\} _0^\infty$ be its associated sequence of orthonormal polynomials. We study the convergence of noninterpolatory integration rules for approximating Cauchy principal value integrals $I(f;\lambda ):=\oint w(x)\frac {{f(x)}}{{x - \lambda }} dx,\quad \lambda \in ( - 1,1).$ This requires investigation of the convergence of the expansion $I(f;\lambda ) \sim \sum \limits _{k = 0}^\infty {(f,{p_k}){q_k}(\lambda ),\quad \lambda \in ( - 1,1),}$ in terms of the functions of the second kind $\{ {q_k}(\lambda )\} _0^\infty$ associated with w, where $(f,{p_k}):=\int _{ - 1}^1 {w(x)f(x){p_k}(x) dx\quad {\text {and}}\quad {q_k}(\lambda } ):=\oint w(x)\frac {{{p_k}(x)}}{{x - \lambda }} dx,$ $k = 0,1,2, \ldots ,\lambda \in ( - 1,1)$.
Similar Articles
• Retrieve articles in Mathematics of Computation with MSC: 41A55, 65D30
• Retrieve articles in all journals with MSC: 41A55, 65D30