An asymptotic approximation for a type of Fourier integral
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- by Paul W. Schmidt PDF
- Math. Comp. 32 (1978), 1171-1182 Request permission
Abstract:
A uniform asymptotic approximation which can be used for all $qh \geqslant 0$ is developed for the Fourier integral \[ I(h) = \int _q^z {\frac {{f(\sqrt {{y^2} - {q^2})} }}{{{{({y^2} - {q^2})}^{1/2}}}}\sin yh dy} \] under the assumptions that $hz > > 1$, that the first $L + 2$ derivatives of $f(y)$ are continuous for $0 \leqslant y \leqslant {({z^2} - {q^2})^{1/2}}$, and that the first $2L + 2$ derivatives of $f(y)$ are continuous at $y = 0$. The approximation is especially convenient when $z > > q$.References
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H. WU & P. W. SCHMIDT, research to be published.
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Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Math. Comp. 32 (1978), 1171-1182
- MSC: Primary 41A60; Secondary 42A76
- DOI: https://doi.org/10.1090/S0025-5718-1978-0510821-9
- MathSciNet review: 0510821