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12 Parabolic Cylinder FunctionsProperties

§12.15 Generalized Parabolic Cylinder Functions

The equation

12.15.1 d2wdz2+(ν+λ-1-λ-2zλ)w=0

can be viewed as a generalization of (12.2.4). This equation arises in the study of non-self-adjoint elliptic boundary-value problems involving an indefinite weight function. See Faierman (1992) for power series and asymptotic expansions of a solution of (12.15.1).