# Help with simple derivation

• Feb 25th 2010, 01:10 AM
wenzhe2092
Help with simple derivation
Hello!

Can anyone assist me in the step by step derivation from
$\displaystyle B_n \cdot sinh(4\lambda_n) = \frac{2}{J_1^2(2\lambda_n)} \int_{0}^{2}\frac{r}{2}J_0(\lambda_n r)f(r)d\left(\frac{r}{2}\right)$

to $\displaystyle B_n=\frac{u_0}{\lambda_n \cdot sinh(4\lambda_n) \cdot J_1(2\lambda_n)}$

with $\displaystyle f(r)=u_o$

Not too sure how it works. Thanks!!
• Feb 25th 2010, 07:19 AM
Jester
Quote:

Originally Posted by wenzhe2092
Hello!

Can anyone assist me in the step by step derivation from
$\displaystyle B_n \cdot sinh(4\lambda_n) = \frac{2}{J_1^2(2\lambda_n)} \int_{0}^{2}\frac{r}{2}J_0(\lambda_n r)f(r)d\left(\frac{r}{2}\right)$

to $\displaystyle B_n=\frac{u_0}{\lambda_n \cdot sinh(4\lambda_n) \cdot J_1(2\lambda_n)}$

with $\displaystyle f(r)=u_o$

Not too sure how it works. Thanks!!

This should get you going

$\displaystyle \int r J_0(\lambda r)\, dr =\frac{r\,J_1(\lambda r)}{\lambda} + c$