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The Quarterly Journal of Mechanics and Applied Mathematics 1981 34(3):311-325; doi:10.1093/qjmam/34.3.311
© 1981 by Oxford University Press
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A GRAPHICAL LOOK AT THE AIRY INTEGRAL

J. H. DE BOER1 and G. P. KÖNNEN2

( 1Department of Mathematics, Catholic University Nijmegen, The Netherlands
2Royal Dutch Meteorological Institute (KNMI) De Bilt, The Netherlands )

As a function of the upper limit s, where f is real-valued, describes a curve in the complex plane. This curve may be studied differential-geometrically in the underlying Euclidean plane. It has are length s and curvaure f'(s) and the transition to its evolute corresponds to integration by parts. This method is used to study the approximation of the Airy integral by a Fresnel integral and yields an estimate for the error.


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