Asymptotic Approximations of Integrals
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Cites background or methods from "Asymptotic Approximations of Integr..."
...Because of its roots in app lied mathematics, the method is well covered by the literature in this area, and we refer to the book s by Olver [465], Henrici [329], or Wong [614] for extensive discussions....
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...Mellin analysis of “harmonic integrals” is a classical topic of applied mathem atics for which we refer to the books by Wong [614] and Paris–Kaminski [472]....
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..., the presen tation in [75, 465, 614]) and the already evoked r ôle of the Airy function....
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...Hayman’s approach [325] which we have expounded here (see also [614]) is notable in its generality as it envisions saddle-point analysis in an abstract perspecti ve, which makes it possible to develop general closure theorems....
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...The proof then proceeds with the analysis of the polylogarit hm whenz= ei (w−π) and s = 1/2+ i t , the integral (48) being estimated asymptotically as a harmonic integral (a continuous analogue of harmonic sums [614]) by means of Me llin transforms....
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Additional excerpts
...[14]), we consider the Toeplitz and the Hankel symbols Tkj = ∫ π...
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