# Toronto Math Forum

## MAT334-2018F => MAT334--Lectures & Home Assignments => Topic started by: Fan Yang on November 14, 2018, 08:30:25 PM

Title: 2.5 Q29
Post by: Fan Yang on November 14, 2018, 08:30:25 PM
Can anyone help me solve 2.5 question 29?
I don't quite understand the hint.
Thank you.
Title: Re: 2.5 Q29
Post by: Zhijian Zhu 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 $s=1:$
$J_n(u) = Re(J_n(u))$
$=Re(\int_{0}^{2\pi}e^{i(usin\theta - n\theta)}d\theta \frac{1}{2\pi})$
$=\int_{0}^{2\pi}cos(usin\theta - n\theta)d\theta\frac{1}{2\pi}$