Bromwich integral
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31: 6.7 Integral Representations
§6.7 Integral Representations
►§6.7(i) Exponential Integrals
… ► ►§6.7(ii) Sine and Cosine Integrals
… ►§6.7(iii) Auxiliary Functions
…32: Sidebar 7.SB1: Diffraction from a Straightedge
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►The intensity distribution follows , where is the Fresnel integral (See 7.3.4).
Fresnel integrals have many applications in optics.
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33: 12.16 Mathematical Applications
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►PCFs are used as basic approximating functions in the theory of contour integrals with a coalescing saddle point and an algebraic singularity, and in the theory of differential equations with two coalescing turning points; see §§2.4(vi) and 2.8(vi).
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►PCFs are also used in integral transforms with respect to the parameter, and inversion formulas exist for kernels containing PCFs.
…Integral transforms and sampling expansions are considered in Jerri (1982).
34: 36.14 Other Physical Applications
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§36.14(i) Caustics
… ►§36.14(ii) Optics
… ►§36.14(iii) Quantum Mechanics
… ►§36.14(iv) Acoustics
…35: 19.6 Special Cases
§19.6 Special Cases
►§19.6(i) Complete Elliptic Integrals
… ►§19.6(ii)
… ►Circular and hyperbolic cases, including Cauchy principal values, are unified by using . … ►§19.6(v)
…36: 19.10 Relations to Other Functions
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►In each case when , the quantity multiplying supplies the asymptotic behavior of the left-hand side as the left-hand side tends to 0.
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