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Mathematics of Computation

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



Quadrature formulae and functions of exponential type

Authors: Qazi I. Rahman and Gerhard Schmeisser
Journal: Math. Comp. 54 (1990), 245-270
MSC: Primary 65D32
MathSciNet review: 990602
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Abstract: In this paper we obtain certain generalizations of the trapezoidal rule and the Euler-Maclaurin formula that involve derivatives. In the case of quadrature of functions of exponential type over infinite intervals we find conditions under which existence of the (improper) integral and convergence of the approximating series become equivalent. In the process, we also establish a best possible version of a theorem of R. P. Boas and A. C. Schaeffer.

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Article copyright: © Copyright 1990 American Mathematical Society