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Weber differential equation

  1. Apr 3, 2010 #1
    Abramovitz presents even and odd solutions to the Weber equation.

    He also presents standard solutions as a pair of parabolic cylinder functions.
    Clearly any linear combination of the even and odd solutions is also a solution of the equation.

    My question is: Why is the parabolic cylinder function so special to be considered a "standard" solution?
    Last edited: Apr 3, 2010
  2. jcsd
  3. Apr 4, 2010 #2
    Can you write this solution?
  4. Apr 4, 2010 #3
    Weber equation

    Even solution

    Odd solution

    where M is the Kummer function.

    Independent parabolic cylinder functions

    [tex]D_\nu(x)[/tex] and [tex]D_{-\nu-1}(ix)[/tex]
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