expansions in Airy functions
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11—20 of 54 matching pages
11: 13.21 Uniform Asymptotic Approximations for Large
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►For a uniform asymptotic expansion in terms of Airy functions for when is large and positive, is real with bounded, and see Olver (1997b, Chapter 11, Ex. 7.3).
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12: 12.14 The Function
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Airy-type Uniform Expansions
…13: 9.8 Modulus and Phase
14: 18.35 Pollaczek Polynomials
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►This expansion is in terms of the Airy function
and its derivative (§9.2), and is uniform in any compact -interval in
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15: 10.72 Mathematical Applications
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►In regions in which (10.72.1) has a simple turning point , that is, and are analytic (or with weaker conditions if is a real variable) and is a simple zero of , asymptotic expansions of the solutions for large can be constructed in terms of Airy functions or equivalently Bessel functions or modified Bessel functions of order (§9.6(i)).
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16: 2.8 Differential Equations with a Parameter
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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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17: 18.34 Bessel Polynomials
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►For uniform asymptotic expansions of as
in terms of Airy functions (§9.2) see Wong and Zhang (1997) and Dunster (2001c).
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