phase shift (or phase)
(0.002 seconds)
11—20 of 42 matching pages
11: 12.9 Asymptotic Expansions for Large Variable
12: 8.20 Asymptotic Expansions of
13: 13.7 Asymptotic Expansions for Large Argument
14: 8.21 Generalized Sine and Cosine Integrals
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►When (and when , in the case of , or , in the case of ) the principal values of , , , and are defined by (8.21.1) and (8.21.2) with the incomplete gamma functions assuming their principal values (§8.2(i)).
Elsewhere in the sector the principal values are defined by analytic continuation from ; compare §4.2(i).
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►When and ,
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►When ,
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►When with (),
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15: 11.11 Asymptotic Expansions of Anger–Weber Functions
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11.11.11
, ,
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16: 13.19 Asymptotic Expansions for Large Argument
17: 15.8 Transformations of Variable
18: 5.11 Asymptotic Expansions
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►As in the sector ,
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►If is complex, then the remainder terms are bounded in magnitude by for (5.11.1), and for (5.11.2), times the first neglected terms.
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►For this result and a similar bound for the sector see Boyd (1994).
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►If in the sector , then
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►Lastly, and again if in the sector , then
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19: 2.11 Remainder Terms; Stokes Phenomenon
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►In both the modulus and phase of the asymptotic variable need to be taken into account.
…Then numerical accuracy will disintegrate as the boundary rays , are approached.
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►In effect, (2.11.7) “corrects” (2.11.6) by introducing a term that is relatively exponentially small in the neighborhood of , is increasingly significant as passes from to , and becomes the dominant contribution after passes .
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►uniformly with respect to in each case.
►The relevant Stokes lines are for , and for .
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