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exponentially-improved expansions

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11: 10.40 Asymptotic Expansions for Large Argument
§10.40(iv) Exponentially-Improved Expansions
12: 9.7 Asymptotic Expansions
§9.7(v) Exponentially-Improved Expansions
13: 7.20 Mathematical Applications
The complementary error function also plays a ubiquitous role in constructing exponentially-improved asymptotic expansions and providing a smooth interpretation of the Stokes phenomenon; see §§2.11(iii) and 2.11(iv). …
14: 10.17 Asymptotic Expansions for Large Argument
§10.17(v) Exponentially-Improved Expansions
15: 5.11 Asymptotic Expansions
§5.11(ii) Error Bounds and Exponential Improvement
16: 10.74 Methods of Computation
Furthermore, the attainable accuracy can be increased substantially by use of the exponentially-improved expansions given in §10.17(v), even more so by application of the hyperasymptotic expansions to be found in the references in that subsection. …
17: 8.12 Uniform Asymptotic Expansions for Large Parameter
c 5 ( 0 ) = 27 45493 81517 36320 .
The last reference also includes an exponentially-improved version (§2.11(iii)) of the expansions (8.12.4) and (8.12.7) for Q ( a , z ) . …
18: Bibliography O
  • F. W. J. Olver (1991a) Uniform, exponentially improved, asymptotic expansions for the generalized exponential integral. SIAM J. Math. Anal. 22 (5), pp. 1460–1474.
  • F. W. J. Olver (1991b) Uniform, exponentially improved, asymptotic expansions for the confluent hypergeometric function and other integral transforms. SIAM J. Math. Anal. 22 (5), pp. 1475–1489.
  • 19: 9.17 Methods of Computation
    However, in the case of Ai ( z ) and Bi ( z ) this accuracy can be increased considerably by use of the exponentially-improved forms of expansion supplied in §9.7(v). …
    20: 12.9 Asymptotic Expansions for Large Variable
    §12.9(ii) Bounds and Re-Expansions for the Remainder Terms