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transition region


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1: 33.12 Asymptotic Expansions for Large η
§33.12(i) Transition Region
2: 10.19 Asymptotic Expansions for Large Order
§10.19(iii) Transition Region
3: 9.16 Physical Applications
The Airy functions constitute uniform approximations whose region of validity includes the turning point and its neighborhood. … These examples of transitions to turbulence are presented in detail in Drazin and Reid (1981) with the problem of hydrodynamic stability. The investigation of the transition between subsonic and supersonic of a two-dimensional gas flow leads to the Euler–Tricomi equation (Landau and Lifshitz (1987)). …
4: 2.8 Differential Equations with a Parameter
The form of the asymptotic expansion depends on the nature of the transition points in 𝐃 , that is, points at which f ( z ) has a zero or singularity. … In Case I there are no transition points in 𝐃 and g ( z ) is analytic. …
§2.8(ii) Case I: No Transition Points
For connection formulas for Liouville–Green approximations across these transition points see Olver (1977b, a, 1978).
§2.8(vi) Coalescing Transition Points