normal form
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1: 31.14 General Fuchsian Equation
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Normal Form
…2: 30.2 Differential Equations
3: 22.18 Mathematical Applications
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►The special case is in Jacobian normal form.
For any two points and on this curve, their sum
, always a third point on the curve, is defined by the Jacobi–Abel addition law
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4: 22.15 Inverse Functions
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►The integrals (22.15.12)–(22.15.14) can be regarded as normal forms for representing the inverse functions.
…can be transformed into normal form by elementary change of variables.
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5: 31.2 Differential Equations
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§31.2(ii) Normal Form of Heun’s Equation
…6: 36.2 Catastrophes and Canonical Integrals
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Normal Forms Associated with Canonical Integrals: Cuspoid Catastrophe with Codimension
… ►Normal Forms for Umbilic Catastrophes with Codimension
… ►For more extensive lists of normal forms of catastrophes (umbilic and beyond) involving two variables (“corank two”) see Arnol’d (1972, 1974, 1975). …7: Bibliography
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Normal forms of functions near degenerate critical points, the Weyl groups and Lagrangian singularities.
Funkcional. Anal. i Priložen. 6 (4), pp. 3–25 (Russian).
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Normal forms of functions in the neighborhood of degenerate critical points.
Uspehi Mat. Nauk 29 (2(176)), pp. 11–49 (Russian).
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Critical points of smooth functions, and their normal forms.
Uspehi Mat. Nauk 30 (5(185)), pp. 3–65 (Russian).
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8: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
9: 19.14 Reduction of General Elliptic Integrals
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►The choice among 21 transformations for final reduction to Legendre’s normal form depends on inequalities involving the limits of integration and the zeros of the cubic or quartic polynomial.
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