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### Messages - Zhijian Zhu

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##### MAT334--Lectures & Home Assignments / Re: 2.5 Q29
« on: November 14, 2018, 08:41:45 PM »
Hi I think this may help you a bit to understand it.
$\overline{G(\bar{z};u)}$
$=\overline{e^{(u/2)(\bar{z}-\frac{1}{\bar{z}})}}$
$=e^{(\frac{u}{2})(z-\frac{1}{\bar{z}})}$
$=G(z;u)$ if u is real.(to prove Hint)
Therefore if u is real,then $J_n(u)$ is real
Then given by (9) with $s=1:$
$J_n(u) = Re(J_n(u))$
$=Re(\int_{0}^{2\pi}e^{i(usin\theta - n\theta)}d\theta \frac{1}{2\pi})$
$=\int_{0}^{2\pi}cos(usin\theta - n\theta)d\theta\frac{1}{2\pi}$

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##### MAT334--Lectures & Home Assignments / 2.5 Q31
« on: November 13, 2018, 10:49:00 PM »
hello, could anyone share the process of doing section2.5 #31?
show that $J_{-n}(-u)=(-1)^nJ_n(u)$
thank you guys！

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##### MAT334--Lectures & Home Assignments / Re: Question 2 from 2.5
« on: November 12, 2018, 10:37:05 AM »
Hi, I got the similar results as yours. I think we are good.

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