Watson lemma

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1: 2.3 Integrals of a Real Variable

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§2.3(ii) Watson’s Lemma

… ►(In other words, differentiation of (2.3.8) with respect to the parameter $\lambda$ (or $\mu$) 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 lemma (§2.3(ii)). …

2: 2.4 Contour Integrals

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§2.4(i) Watson’s Lemma

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3: 6.12 Asymptotic Expansions

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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

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6: 8.21 Generalized Sine and Cosine Integrals

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7: 13.8 Asymptotic Approximations for Large Parameters

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8: Bibliography S

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Asymptotic expansions of Mellin transforms and analogues of Watson’s lemma. SIAM J. Math. Anal. 16 (4), pp. 896–906.

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External Links:

ISSN 0036-1410, Document, Link, MathReview (John S. Lew), ZentralBlatt

Referenced by:

§2.3(vi).

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9: 2.11 Remainder Terms; Stokes Phenomenon

… ►Application of Watson’s lemma (§2.4(i)) yields …

10: 2.6 Distributional Methods

… ►Motivated by Watson’s lemma (§2.3(ii)), we substitute (2.6.2) in (2.6.1), and integrate term by term. …