- #1
spacetimedude
- 88
- 1
Show that $$\int_0^\infty dx\exp(ikx^3) , k>0$$ may be written as integral from 0 to ##\infty## along the line ##arg(z) = \frac{\pi}{6}##.
I'd appreciate it if you can help me how to approach this problem. My initial impression was to expand the integrand out
$$\sum^{\infty}_{n=0}\frac{(ikx^3)^n}{n!}$$
but did not how to obtain the ##arg(z)## condition. I plugged the integral in wolframalpha and gave me an expression with a Gamma function, which the lecture has covered but I'm not sure how to apply here.
Thanks
I'd appreciate it if you can help me how to approach this problem. My initial impression was to expand the integrand out
$$\sum^{\infty}_{n=0}\frac{(ikx^3)^n}{n!}$$
but did not how to obtain the ##arg(z)## condition. I plugged the integral in wolframalpha and gave me an expression with a Gamma function, which the lecture has covered but I'm not sure how to apply here.
Thanks