Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: Extension to parabolic cylinder functions?
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
Leslaw Bieniasz

Posts: 171
Registered: 12/13/04
Extension to parabolic cylinder functions?
Posted: Feb 9, 2012 6:15 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply



Hi,

The so-called parabolic cylinder functions are known to represent
the solutions of the ordinary differential equation

d^2 u(x)/ dx^2 -(a*x^2 +b*x + c) * u(x) = 0

When a = 0 the equation reduces to the Airy equation, with
Airy functions as solutions.

I am trying to solve and equation with a fourth order polynomial
in the place of the second order one:

d^2 u(x)/ dx^2 -(a*x^4 + b*x^3 + c*x^2 + d*x + e) * u(x) = 0

My question is: are there any extensions of the parabolic
cylinder functions to the above equation? Do there exist
any special functions that represent solutions of the equation?

I would appreciate any pointers.

Leslaw



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.