Quadrature Formulae and Functions of Exponential Type
- 1 January 1990
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 54 (189) , 245-270
- https://doi.org/10.2307/2008693
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.Keywords
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