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A Hermite differential equation

  1. Mar 20, 2016 #1
    y" - 2xy' + my = 0 this is well known hermite diff eqn. now can anyone tell me what kind of conts is m?? what is the suitable value of m??
    Last edited: Mar 20, 2016
  2. jcsd
  3. Mar 20, 2016 #2
    please explain what is 'm'?
  4. Mar 20, 2016 #3
    sorry for the confusion.. I made the correction in my qus...
  5. Mar 20, 2016 #4


    Staff: Mentor

    Several web pages that I looked at say that m is usually a nonnegative integer. Did you try searching for yourself?
  6. Mar 20, 2016 #5
    This is Hermite’s equation, where special choices of m give rise to the Hermite polynomials.
    there exists a polynomial solution of the original equation whenever m = 2n , n = 0,1,2 , , , ... . With the choice m = 2n , and the arbitrary multiplicative constant chosen so that the coefficient of the term x^n is 2^(m/2)
  7. Mar 20, 2016 #6
    @mrinmoy Pl. see a detail analysis
    in < http://www.ncl.ac.uk/maths/students/teaching/notebooks/SeriesSolnNotebook.pdf> [Broken]
    Last edited by a moderator: May 7, 2017
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