Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


The remainder term for analytic functions of symmetric Gaussian quadratures
HTML articles powered by AMS MathViewer

by Thomas Schira PDF
Math. Comp. 66 (1997), 297-310 Request permission


For analytic functions the remainder term of Gaussian quadrature rules can be expressed as a contour integral with kernel $K_n$. In this paper the kernel is studied on elliptic contours for a great variety of symmetric weight functions including especially Gegenbauer weight functions. First a new series representation of the kernel is developed and analyzed. Then the location of the maximum modulus of the kernel on suitable ellipses is determined. Depending on the weight function the maximum modulus is attained at the intersection point of the ellipse with either the real or imaginary axis. Finally, a detailed discussion for some special weight functions is given.
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (1991): 41A55, 65D30, 65D32
  • Retrieve articles in all journals with MSC (1991): 41A55, 65D30, 65D32
Additional Information
  • Thomas Schira
  • Affiliation: Institut für Praktische Mathematik, Universität Karlsruhe, D–76128 Karlsruhe, Germany
  • Email:
  • Received by editor(s): February 12, 1995
  • Received by editor(s) in revised form: January 26, 1996
  • © Copyright 1997 American Mathematical Society
  • Journal: Math. Comp. 66 (1997), 297-310
  • MSC (1991): Primary 41A55; Secondary 65D30, 65D32
  • DOI:
  • MathSciNet review: 1372009