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Orthogonality and find coefficients

  • #1

Homework Statement


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

Homework 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.

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?

Homework Statement





Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
Gold Member
5,002
6

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?
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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