About the Project

isolated essential


(0.001 seconds)

3 matching pages

1: 1.10 Functions of a Complex Variable
Lastly, if a n 0 for infinitely many negative n , then z 0 is an isolated essential singularity. … In any neighborhood of an isolated essential singularity, however small, an analytic function assumes every value in with at most one exception. …
2: 32.2 Differential Equations
An equation is said to have the Painlevé property if all its solutions are free from movable branch points; the solutions may have movable poles or movable isolated essential singularities (§1.10(iii)), however. …
3: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
Often circumstances allow rather stronger statements, such as uniform convergence, or pointwise convergence at points where f ( x ) is continuous, with convergence to ( f ( x 0 ) + f ( x 0 + ) ) / 2 if x 0 is an isolated point of discontinuity. … An essential feature of such symmetric operators is that their eigenvalues λ are real, and eigenfunctions … In unusual cases N = , even for all , such as in the case of the Schrödinger–Coulomb problem ( V = r 1 ) discussed in §18.39 and §33.14, where the point spectrum actually accumulates at the onset of the continuum at λ = 0 , implying an essential singularity, as well as a branch point, in matrix elements of the resolvent, (1.18.66). … If T T = T then T is essentially self-adjoint and if T = T then T is self-adjoint. …