- #1

MathematicalPhysicist

Gold Member

- 4,287

- 202

## Main Question or Discussion Point

I want to show that: [tex]Ai(x)+jAi(jx)+j^2Ai(j^2x)=0[/tex], where:

[tex]Ai(x)=\int_{-i\infty}^{i\infty}e^{xz-z^3/3}dz[/tex] and [tex]j=e^{2i\pi/3}[/tex], so far I got that I need to show that:

[tex]e^{zx}+je^{jxz}+j^2e^{xzj^2}=0[/tex] but didn't succeed in doing so.

Any hints?

[tex]Ai(x)=\int_{-i\infty}^{i\infty}e^{xz-z^3/3}dz[/tex] and [tex]j=e^{2i\pi/3}[/tex], so far I got that I need to show that:

[tex]e^{zx}+je^{jxz}+j^2e^{xzj^2}=0[/tex] but didn't succeed in doing so.

Any hints?