for large ℜz
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1—10 of 132 matching pages
1: 16.22 Asymptotic Expansions
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►Asymptotic expansions of for large
are given in Luke (1969a, §§5.7 and 5.10) and Luke (1975, §5.9).
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2: 28.34 Methods of Computation
3: 8.20 Asymptotic Expansions of
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§8.20(i) Large
…4: 28.25 Asymptotic Expansions for Large
§28.25 Asymptotic Expansions for Large
…5: 8.25 Methods of Computation
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►Although the series expansions in §§8.7, 8.19(iv), and 8.21(vi) converge for all finite values of , they are cumbersome to use when is large owing to slowness of convergence and cancellation.
For large
the corresponding asymptotic expansions (generally divergent) are used instead.
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6: 5.19 Mathematical Applications
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►By translating the contour parallel to itself and summing the residues of the integrand, asymptotic expansions of for large
, or small , can be obtained complete with an integral representation of the error term.
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7: 8.11 Asymptotic Approximations and Expansions
8: 11.13 Methods of Computation
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►Although the power-series expansions (11.2.1) and (11.2.2), and the Bessel-function expansions of §11.4(iv) converge for all finite values of , they are cumbersome to use when is large owing to slowness of convergence and cancellation.
For large
and/or the asymptotic expansions given in §11.6 should be used instead.
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9: 9.17 Methods of Computation
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►Although the Maclaurin-series expansions of §§9.4 and 9.12(vi) converge for all finite values of , they are cumbersome to use when is large owing to slowness of convergence and cancellation.
For large
the asymptotic expansions of §§9.7 and 9.12(viii) should be used instead.
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