The parabolic cylinder differential equation is the second-order
ordinary differential equation
(1)
whose solution is given by
(2)
where is a parabolic
cylinder function .
The generalized parabolic cylinder differential equation is the differential equation of the form
(3)
(Abramowitz and Stegun 1972, p. 686; Zwillinger 1995, p. 414; Zwillinger 1997, p. 126) whose solution can be expressed in terms of parabolic
cylinder functions as
(4)
where
(5)
See also Parabolic Cylinder Function ,
Parabolic Cylindrical Coordinates
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References Abramowitz, M. and Stegun, I. A. (Eds.). "Parabolic Cylinder Function." Ch. 19 in Handbook
of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, pp. 685-700, 1972. Zwillinger, D. (Ed.). CRC
Standard Mathematical Tables and Formulae. Boca Raton, FL: CRC Press, p. 414,
1995. Zwillinger, D. Handbook
of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 126,
1997. Referenced on Wolfram|Alpha Parabolic Cylinder
Differential Equation
Cite this as:
Weisstein, Eric W. "Parabolic Cylinder Differential Equation." From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/ParabolicCylinderDifferentialEquation.html
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