# §12.15 Generalized Parabolic Cylinder Functions

The equation

 12.15.1 $\frac{{d}^{2}w}{{dz}^{2}}+\left(\nu+\lambda^{-1}-\lambda^{-2}z^{\lambda}\right% )w=0$

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).