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Mathematics of Computation

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Some extensions of Legendre quadrature

Author: A. C. R. Newbery
Journal: Math. Comp. 23 (1969), 173-176
MSC: Primary 65.55
MathSciNet review: 0238492
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Abstract: The $ m$-point Gauss-Legendre formula gives an exact expression for the integral of an algebraic polynomial of maximum degree $ 2m - 1$ in terms of $ m$ ordinates. It is shown that analogous formulas can be derived for exponential and trigonometric polynomials.

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

  • [1] E. Isaacson & H. B. Keller, Analysis of Numerical Methods, Wiley, New York, 1966. MR 34 #924. MR 0201039 (34:924)
  • [2] G. Birkhoff, D. M. Young & E. H. Zarantonello, Numerical Methods in Conformal Mapping, Proc. Sympos. Appl. Math., Vol. 4; Fluid Dynamics, McGraw-Hill, New York, 1953, pp. 117-40. MR 15, 258. MR 0057637 (15:258b)
  • [3] F. B. Hildebrand, Introduction to Numerical Analysis, McGraw-Hill, NewYork, 1956. MR 17, 788. MR 0075670 (17:788d)

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Article copyright: © Copyright 1969 American Mathematical Society

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