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1: 2.3 Integrals of a Real Variable
§2.3(ii) Watson’s Lemma
(In other words, differentiation of (2.3.8) with respect to the parameter λ (or μ ) is legitimate.) … Watson’s lemma can be regarded as a special case of this result. For error bounds for Watson’s lemma and Laplace’s method see Boyd (1993) and Olver (1997b, Chapter 3). … The first result is the analog of Watson’s lemma2.3(ii)). …
2: 2.4 Contour Integrals
§2.4(i) Watson’s Lemma
3: 6.12 Asymptotic Expansions
4: 11.6 Asymptotic Expansions
See also Watson (1944, p. 336). … and for an estimate of the relative error in this approximation see Watson (1944, p. 336).
5: 7.12 Asymptotic Expansions
6: 8.21 Generalized Sine and Cosine Integrals
7: 13.8 Asymptotic Approximations for Large Parameters
8: Bibliography S
  • A. Sidi (1985) Asymptotic expansions of Mellin transforms and analogues of Watson’s lemma. SIAM J. Math. Anal. 16 (4), pp. 896–906.
  • 9: 2.11 Remainder Terms; Stokes Phenomenon
    Application of Watson’s lemma2.4(i)) yields …
    10: 2.6 Distributional Methods
    Motivated by Watson’s lemma2.3(ii)), we substitute (2.6.2) in (2.6.1), and integrate term by term. …