canonical denominator (or numerator)
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1: 36.2 Catastrophes and Canonical Integrals
§36.2 Catastrophes and Canonical Integrals
►§36.2(i) Definitions
… ►Canonical Integrals
… ►§36.2(ii) Special Cases
… ►§36.2(iii) Symmetries
…2: 36.3 Visualizations of Canonical Integrals
§36.3 Visualizations of Canonical Integrals
►§36.3(i) Canonical Integrals: Modulus
… ►§36.3(ii) Canonical Integrals: Phase
►In Figure 36.3.13(a) points of confluence of phase contours are zeros of ; similarly for other contour plots in this subsection. In Figure 36.3.13(b) points of confluence of all colors are zeros of ; similarly for other density plots in this subsection. …3: 1.12 Continued Fractions
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1.12.4
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and are called the th (canonical) numerator and denominator respectively.
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1.12.7
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1.12.8
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4: 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
…5: 36.10 Differential Equations
§36.10 Differential Equations
►§36.10(i) Equations for
►In terms of the normal form (36.2.1) the satisfy the operator equation … ► , swallowtail: … ►In terms of the normal forms (36.2.2) and (36.2.3), the satisfy the following operator equations …6: 36.9 Integral Identities
7: 36.1 Special Notation
§36.1 Special Notation
… ►The main functions covered in this chapter are cuspoid catastrophes ; umbilic catastrophes with codimension three , ; canonical integrals , , ; diffraction catastrophes , , generated by the catastrophes. …8: 36.6 Scaling Relations
9: 36.11 Leading-Order Asymptotics
§36.11 Leading-Order Asymptotics
… ►and far from the bifurcation set, the cuspoid canonical integrals are approximated by … ►
36.11.5
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36.11.7
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36.11.8
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