# §12.15 Generalized Parabolic Cylinder Functions

The equation

 12.15.1 $\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+\left(\nu+\lambda^{-1}-\lambda^{-2% }z^{\lambda}\right)w=0$ ⓘ Symbols: $\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}$: derivative of $f$ with respect to $x$, $z$: complex variable and $\nu$: real or complex parameter Referenced by: §12.15 Permalink: http://dlmf.nist.gov/12.15.E1 Encodings: TeX, pMML, png See also: Annotations for 12.15 and 12

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).