12 Parabolic Cylinder Functions Properties 12.14 The Function $\mathop{W\/}\nolimits\!\left(a,x\right)$ 12.16 Mathematical Applications

§12.15 Generalized Parabolic Cylinder Functions

Keywords:: parabolic cylinder functions
Permalink:: http://dlmf.nist.gov/12.15

The equation

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

Symbols:: $\frac{df}{dx}$ : 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

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).

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