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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.


On accelerating the convergence of infinite double series and integrals
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by David Levin PDF
Math. Comp. 35 (1980), 1331-1345 Request permission


The generalization of Shanks’ e-transformation to double series is discussed and a class of nonlinear transformations, the ${[A/S]_R}$ transformations, for accelerating the convergence of infinite double series is presented. It is constructed so as to sum exactly infinite double series whose terms satisfy certain finite linear double difference equations; in that sense it is a generalization of Shanks’ e-transformation or its equivalent Wynn’s $\varepsilon$-algorithm. A generalization of the ${[A/S]_R}$ transformation to N-dimensional series is also presented and their application to power series is discussed and exemplified. Some transformations for accelerating the convergence of infinite double integrals are also obtained, generalizing the confluent $\varepsilon$-algorithm of Wynn and the G-transformation of Gray, Atchison, and McWilliams for infinite 1-D integrals.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 35 (1980), 1331-1345
  • MSC: Primary 65B10; Secondary 65D15
  • DOI:
  • MathSciNet review: 583511