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Bessel's Equation Solution Proof

  1. Apr 17, 2005 #1
    hi there ,

    i need the proof of the j(x) function starting from Bessel's Differential Equation .

    and if anyone has any Online free book , or research on Bessel for first , second and Hankel in DETAILS , plz tell me about it .

    Thanks .
     
  2. jcsd
  3. Apr 17, 2005 #2

    Hurkyl

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    "Proving a function" is nonsensical -- what are you trying to ask?
     
  4. Apr 17, 2005 #3

    dextercioby

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  5. Apr 17, 2005 #4

    dextercioby

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  6. Apr 17, 2005 #5
    I mean the derivation of the Differential bessel equation
    in order to end with J(x) .
     
  7. Apr 17, 2005 #6

    dextercioby

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    U mean how to get the Bessel ODE starting from where?

    Daniel.
     
  8. Apr 17, 2005 #7

    saltydog

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    I think you mean: starting with Bessel's ODE, and using power series, and all of the tough work adjusting the series to look like the Bessel functions.
     
  9. Apr 18, 2005 #8
    exactly , as you said ,

    any one help .
     
  10. Apr 18, 2005 #9

    arildno

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    hi, mostafa:
    Start with posting the differential equation, and show what you have done so far (preferably in the LATEX format).

    There are plenty of us who know how this should be done, but it is forum policy (and beneficial to yourself) that you do most on your own, and that we help you at those particular places you're stuck.
     
  11. Apr 18, 2005 #10

    HallsofIvy

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    Actually, J(x) (more generally Jn(x)]) is defined as the solution to Bessel's equation. That J(x) is a certain power series could be proven using Frobenius' method.
     
  12. Apr 18, 2005 #11
    yes , but i don't know how to write latex .
     
  13. Apr 18, 2005 #12

    dextercioby

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    If u're gonna keep posting math/physics related subjects here,please learn LaTex,it's not difficult.

    Daniel.
     
  14. Apr 19, 2005 #13
    start with power series y=x^m(sigma an x^n)
     
  15. Apr 19, 2005 #14
    Hi friends,
    I am struggling on the concepts of fourier integral transforms.
    Anyone who knew can sent to me.
    thanks
     
  16. Apr 20, 2005 #15
    erwin kreziog advanced engineering mathematics book is very nice
     
  17. Oct 6, 2009 #16
    Another book that discusses neatly the Bessel ODE is Differential Equations by Lomen and Mark. It gives all basic details, definitions and theorems (without proofs) that are required to solve the problem. This book assumes that you have already done a basic course in Calculus are comfortable with concepts on Sequences and Series.
     
  18. Jun 29, 2011 #17
    I had the same question...

    I found this book online. Author is Erwin Kreysig.
    Adavanced Engineering Mathematics. page 182.
    Nice book! Thanks for the tip.

    Wikipedia doesn't give any derivation.
    Mathworld gives some more color but it's still rather foggy.
    There's a soundless video on YouTube that explains a little more...


    Yours,

    Raj
     
    Last edited by a moderator: Sep 25, 2014
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