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fold canonical integral

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1: 36.2 Catastrophes and Canonical Integrals
Normal Forms Associated with Canonical Integrals: Cuspoid Catastrophe with Codimension K
Canonical Integrals
Ψ 1 is related to the Airy function (§9.2): …
2: 36.7 Zeros
§36.7(i) Fold Canonical Integral
3: 36.9 Integral Identities
§36.9 Integral Identities
4: 36.4 Bifurcation Sets
K = 1 , fold bifurcation set: …
5: 36.10 Differential Equations
6: 36.6 Scaling Relations
§36.6 Scaling Relations
Ψ K ( x ; k ) = k β K Ψ K ( y ( k ) ) ,
Ψ ( U ) ( x ; k ) = k β ( U ) Ψ ( U ) ( y ( U ) ( k ) ) ,
Indices for k -Scaling of Magnitude of Ψ K or Ψ ( U ) (Singularity Index)
Table 36.6.1: Special cases of scaling exponents for cuspoids.
singularity K β K γ 1 K γ 2 K γ 3 K γ K
fold 1 1 6 2 3 - - 2 3