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}##.(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Integral e^(ikx^3)

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Integral ikx^3 | Date |
---|---|

I Solving an integral | Monday at 4:38 PM |

I Integrate a function over a closed circle-like contour around an arbitrary point on a torus | Saturday at 12:51 PM |

A Integrate f(x) = tanh(c*x^b)? Wolfram says not possible ... | Mar 11, 2018 |

I Looking for additional material about limits and distributions | Feb 17, 2018 |

B What's the derivative of sin^3(x+1) ^2? | Dec 31, 2017 |

**Physics Forums - The Fusion of Science and Community**