12 Parabolic Cylinder Functions Properties 12.14 The Function $W\left(a,x\right)$ 12.16 Mathematical Applications

§12.15 Generalized Parabolic Cylinder Functions

ⓘ

Keywords:: generalized, parabolic cylinder functions
Permalink:: http://dlmf.nist.gov/12.15
See also:: Annotations for Ch.12

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 with respect to , : 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 Ch.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).

12.14 The Function $W\left(a,x\right)$ 12.16 Mathematical Applications

Site Privacy Accessibility Privacy Program Copyrights Vulnerability Disclosure No Fear Act Policy FOIA Environmental Policy Scientific Integrity Information Quality Standards Commerce.gov Science.gov USA.gov