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Orthogonality and find coefficients

  1. May 20, 2009 #1
    1. The problem statement, all variables and given/known data
    I have that the general solution of a function is
    f([tex]\rho[/tex],t)=[tex]\Sigma[/tex]c(m)Jo([tex]\alpha\rho\a[/tex]) exp[-Dtm^2]
    where c(m) are constants.
    I need to find an expression for c(m) in terms of an integral

    2. Relevant equations
    Orthogonality relation given is
    [tex]\int[/tex]dx x Jo([tex]\alpha(m)*x/a[/tex])Jo([tex]\alpha(q)*x/a[/tex] = 0.5a^2 J1([tex]\alpha[/tex])[tex]\delta(mq)[/tex] where the integral runs between 0 and a and the subscripts on alphas are m and q respectively.

    3. The attempt at a solution
    I know that you can multiply both sides of the first equation by Jo([tex]\alpha*x/a[/tex] *x and integrate both sides over the range, using the sifting property given but what happens to the exponential term from the original equation?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 20, 2009 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    The exponential term is independent of your integration variable, [itex]x[/itex] and therefor is constant and it comes outside your integral.
     
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