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Math Help - Help with simple derivation

  1. #1
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    Help with simple derivation

    Hello!

    Can anyone assist me in the step by step derivation from
    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)<br />

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

    with f(r)=u_o

    Not too sure how it works. Thanks!!
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  2. #2
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    Quote Originally Posted by wenzhe2092 View Post
    Hello!

    Can anyone assist me in the step by step derivation from
    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)<br />

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

    with f(r)=u_o

    Not too sure how it works. Thanks!!
    This should get you going

     <br />
\int r J_0(\lambda r)\, dr =\frac{r\,J_1(\lambda r)}{\lambda} + c<br />
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