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Parabolic cylinder functions and parabolic functions

  • Wilhelm Magnus
  • Fritz Oberhettinger
  • Raj Pal Soni
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 52)

Abstract

The parabolic cylinder functions may, in general, be considered as solutions of the differential equation
$$\frac{{{d^2}y}}{{d{x^2}}} + (a{x^2} + bx + c)y = 0$$
(1)
which, by a simple change of variable, reduces to the form
$$\frac{{{d^2}y}}{{d{x^2}}} + (v + \frac{1}{2} - \frac{1}{4}{z^2}) = 0.$$
(2)
.

Keywords

Recurrence Relation Chapter VIII Differentiation Formula Whittaker Function Parabolic Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature

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  6. Erdélyi, A.: Higher transcendental functions, Vol. 2. New York: McGraw-Hill 1953.Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1966

Authors and Affiliations

  • Wilhelm Magnus
    • 1
  • Fritz Oberhettinger
    • 2
  • Raj Pal Soni
    • 3
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityUSA
  2. 2.Oregon State UniversityUSA
  3. 3.International Business Machines CorporationUSA

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