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# Numerical Indefinite Integration of Functions with Singularities

Aeyoung Park Jang and Seymour Haber
Mathematics of Computation
Vol. 70, No. 233 (Jan., 2001), pp. 205-221
Stable URL: http://www.jstor.org/stable/2698930
Page Count: 17
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## Abstract

We derive an indefinite quadrature formula, based on a theorem of Ganelius, for Hp functions, for p > 1, over the interval (-1, 1). The main factor in the error of our indefinite quadrature formula is O(e$^{- \pi \sqrt {N/q}}$), with 2N nodes and 1/p + 1/q = 1. The convergence rate of our formula is better than that of the Stenger-type formulas by a factor of $\sqrt {2}$ in the constant of the exponential. We conjecture that our formula has the best possible value for that constant. The results of numerical examples show that our indefinite quadrature formula is better than Haber's indefinite quadrature formula for Hp-functions.

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