Airy functions
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11: Sidebar 9.SB2: Interference Patterns in Caustics
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►The oscillating intensity of the interference fringes across the caustic is described by the Airy function.
12: 9.13 Generalized Airy Functions
§9.13 Generalized Airy Functions
►§9.13(i) Generalizations from the Differential Equation
… ► ►§9.13(ii) Generalizations from Integral Representations
… ►13: 9.10 Integrals
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§9.10(i) Indefinite Integrals
… ►§9.10(ii) Asymptotic Approximations
… ►§9.10(iv) Definite Integrals
… ►§9.10(v) Laplace Transforms
… ►§9.10(vi) Mellin Transform
…14: 9.17 Methods of Computation
§9.17 Methods of Computation
… ►Among the integral representations of the Airy functions the Stieltjes transform (9.10.18) furnishes a way of computing in the complex plane, once values of this function can be generated on the positive real axis. … ►§9.17(v) Zeros
►Zeros of the Airy functions, and their derivatives, can be computed to high precision via Newton’s rule (§3.8(ii)) or Halley’s rule (§3.8(v)), using values supplied by the asymptotic expansions of §9.9(iv) as initial approximations. … ►For the computation of the zeros of the Scorer functions and their derivatives see Gil et al. (2003c).15: 9.12 Scorer Functions
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9.12.4
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9.12.5
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is a numerically satisfactory companion to the complementary functions
and on the interval .
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9.12.8
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9.12.11
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16: 9.4 Maclaurin Series
17: 9.9 Zeros
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§9.9(ii) Relation to Modulus and Phase
… ►§9.9(iii) Derivatives With Respect to
… ►§9.9(iv) Asymptotic Expansions
… ►§9.9(v) Tables
… ►18: 9.6 Relations to Other Functions
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§9.6(i) Airy Functions as Bessel Functions, Hankel Functions, and Modified Bessel Functions
… ►§9.6(ii) Bessel Functions, Hankel Functions, and Modified Bessel Functions as Airy Functions
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9.6.20
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