A sinc approximation for the indefinite integral
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- by Ralph Baker Kearfott PDF
- Math. Comp. 41 (1983), 559-572 Request permission
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
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M. Abramowitz & I. A. Stegun, Editors, Handbook of Mathematical Functions, Dover, New York, 1970.
- Frank Stenger, Approximations via Whittaker’s cardinal function, J. Approximation Theory 17 (1976), no. 3, 222–240. MR 481786, DOI 10.1016/0021-9045(76)90086-1
- Frank Stenger, Optimal convergence of minimum norm approximations in $H_{p}$, Numer. Math. 29 (1977/78), no. 4, 345–362. MR 483329, DOI 10.1007/BF01432874
- Frank Stenger, Numerical methods based on Whittaker cardinal, or sinc functions, SIAM Rev. 23 (1981), no. 2, 165–224. MR 618638, DOI 10.1137/1023037 F. Stenger, private communication.
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Math. Comp. 41 (1983), 559-572
- MSC: Primary 65D30; Secondary 41A99
- DOI: https://doi.org/10.1090/S0025-5718-1983-0717703-X
- MathSciNet review: 717703