Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

Adjusted Forms of the Fourier Coefficient Asymptotic Expansion and Applications in Numerical Quadrature

J. N. Lyness
Mathematics of Computation
Vol. 25, No. 113 (Jan., 1971), pp. 87-104
DOI: 10.2307/2005134
Stable URL: http://www.jstor.org/stable/2005134
Page Count: 18
  • Read Online (Free)
  • Download ($34.00)
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Adjusted Forms of the Fourier Coefficient Asymptotic Expansion and Applications in Numerical Quadrature
Preview not available

Abstract

The conventional Fourier coefficient asymptotic expansion is derived by means of a specific contour integration. An adjusted expansion is obtained by deforming this contour. A corresponding adjustment to the Euler-Maclaurin expansion exists. The effect of this adjustment in the error functional for a general quadrature rule is investigated. It is the same as the effect of subtracting out a pair of complex poles from the integrand, using an unconventional subtraction function. In certain applications, the use of this subtraction function is of practical value. An incidental result is a direct proof of Erdélyi's formula for the Fourier coefficient asymptotic expansion, valid when f(x) has algebraic or logarithmic singularities, but is otherwise analytic.

Page Thumbnails

  • Thumbnail: Page 
87
    87
  • Thumbnail: Page 
88
    88
  • Thumbnail: Page 
89
    89
  • Thumbnail: Page 
90
    90
  • Thumbnail: Page 
91
    91
  • Thumbnail: Page 
92
    92
  • Thumbnail: Page 
93
    93
  • Thumbnail: Page 
94
    94
  • Thumbnail: Page 
95
    95
  • Thumbnail: Page 
96
    96
  • Thumbnail: Page 
97
    97
  • Thumbnail: Page 
98
    98
  • Thumbnail: Page 
99
    99
  • Thumbnail: Page 
100
    100
  • Thumbnail: Page 
101
    101
  • Thumbnail: Page 
102
    102
  • Thumbnail: Page 
103
    103
  • Thumbnail: Page 
104
    104