Parabolic Cylinder Differential Equation
المؤلف:
Abramowitz, M. and Stegun, I. A
المصدر:
"Parabolic Cylinder Function." Ch. 19 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover
الجزء والصفحة:
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3-7-2018
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Parabolic Cylinder Differential Equation
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
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.
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