Numerical integration formulas for use with weight functions $x^{2}$ and $x/\surd (1-x^{2})$
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- by R. E. Greenwood, P. D. M. Carnahan and J. W. Nolley PDF
- Math. Comp. 13 (1959), 37-40 Request permission
References
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P. L. Chebyshev, “Sur les Quadratures,” JOURNAL de MATHEMATIQUES PURES ET APPLIQUE Series 2, vol. 19 (1874), p. 19-34, or OEUVRES, vol. II, pp. 165-180. (St. Petersberg, 1907). Many errors in the JOURNAL article have been corrected in the OEUVRES, so that when a choice is possible it is suggested that OEUVRES be used as a reference. (The Library of Congress has recently standardized the transliteration into Latin characters from Cyrillic characters. The above version Chebyshev would appear to be their preferred spelling.) The referee reports that Chebyshev’s papers were reprinted in Russian in 1948, and that the above appears in Volume II of his works, pp. 49-62.
- Herbert E. Salzer, Tables for facilitating the use of Chebyshev’s quadrature formula, J. Math. Phys. Mass. Inst. Tech. 26 (1947), 191–194. MR 22718, DOI 10.1002/sapm1947261191
- Robert E. Greenwood and Masil B. Danford, Numerical integration with a weight function $x$, J. Math. Physics 28 (1949), 99–106. MR 0030817, DOI 10.1002/sapm194928199 Paul D. M. Carnahan, “Numerical Integration with the Weight Function $x/\sqrt {1 - {x^2}}$,” unpublished Master’s thesis, The University of Texas, May 1949. Joe Walter Nolley, “Concerning Numerical Integration on the Range $( - 1, + 1)$ with the Weight Function ${x^2}$,” unpublished Master’s thesis, The University of Texas, May 1958.
Additional Information
- © Copyright 1959 American Mathematical Society
- Journal: Math. Comp. 13 (1959), 37-40
- MSC: Primary 65.00
- DOI: https://doi.org/10.1090/S0025-5718-1959-0102174-3
- MathSciNet review: 0102174