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Mathematics of Computation

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A sinc approximation for the indefinite integral

Author: Ralph Baker Kearfott
Journal: Math. Comp. 41 (1983), 559-572
MSC: Primary 65D30; Secondary 41A99
MathSciNet review: 717703
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Abstract: A method for computing $ \smallint _0^xf(t)\;dt,x = (0,1)$ is outlined, where $ f(t)$ may have singularities at $ t = 0$ and $ t = 1$. The method depends on the approximation properties of Whittaker cardinal, or sinc function expansions; the general technique may be used for semi-infinite or infinite intervals in addition to (0,1). Tables of numerical results are given.

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

  • [1] M. Abramowitz & I. A. Stegun, Editors, Handbook of Mathematical Functions, Dover, New York, 1970.
  • [2] Frank Stenger, Approximations via Whittaker’s cardinal function, J. Approximation Theory 17 (1976), no. 3, 222–240. MR 0481786
  • [3] Frank Stenger, Optimal convergence of minimum norm approximations in 𝐻_{𝑝}, Numer. Math. 29 (1977/78), no. 4, 345–362. MR 0483329
  • [4] Frank Stenger, Numerical methods based on Whittaker cardinal, or sinc functions, SIAM Rev. 23 (1981), no. 2, 165–224. MR 618638, 10.1137/1023037
  • [5] F. Stenger, private communication.

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Keywords: Indefinite integrals, singular integrals, quadrature, sine functions, Whittaker's cardinal function, approximation theory
Article copyright: © Copyright 1983 American Mathematical Society