12 Parabolic Cylinder FunctionsProperties12.14 The Function $W\left(a,x\right)$12.16 Mathematical Applications

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).