- #1
the_dialogue
- 79
- 0
Homework Statement
[tex]
\int_{0}^{b} \int_{0}^{2\pi} C_{k,m}(r)^2 \left{\begin{array}{cc}cos(m\theta)^2\\sin(m\theta)^2 \end{array}\right} r dr d\theta
[/tex]
Homework Equations
See above
The Attempt at a Solution
Ignoring the 'r' integral for a second, the solution that I see written here is:
[tex]\pi(1+\delta_{0,m}(\int_{0}^{b} C_{k,m}(r)^2 r dr)[/tex]
where [tex]\delta[/tex] is Kronecker delta.
Where did the tex]\pi(1+\delta_(0,m)}[/tex] come from?
I suppose my confusion may strand from misunderstanding what the bracketed term [tex]\left{\begin{array}{cc}cos(m\theta)^2\\sin(m\theta)^2 \end{array}\right}[/tex] means. What is this notation? Instinct says column vector, but that of course doesn't seem to be the case.
Thank you for any help!