Airy functions
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21: 9.18 Tables
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§9.18(ii) Real Variables
… ►§9.18(iii) Complex Variables
… ►§9.18(iv) Zeros
… ►§9.18(v) Integrals
… ►§9.18(vii) Generalized Airy Functions
…22: 9 Airy and Related Functions
Chapter 9 Airy and Related Functions
…23: 36.9 Integral Identities
24: 2.8 Differential Equations with a Parameter
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►These are elementary functions in Case I, and Airy functions (§9.2) in Case II.
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2.8.19
►of smallest absolute value, and define the envelopes of and by
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2.8.20
,
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►For other examples of uniform asymptotic approximations and expansions of special functions in terms of Airy functions see especially §10.20 and §§12.10(vii), 12.10(viii); also §§12.14(ix), 13.20(v), 13.21(iii), 13.21(iv), 15.12(iii), 18.15(iv), 30.9(i), 30.9(ii), 32.11(ii), 32.11(iii), 33.12(i), 33.12(ii), 33.20(iv), 36.12(ii), 36.13.
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25: 33.12 Asymptotic Expansions for Large
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►Then as ,
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33.12.2
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33.12.3
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►Here and are the Airy functions (§9.2), and
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►The first set is in terms of Airy functions and the expansions are uniform for fixed and , where is an arbitrary small positive constant.
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