User blog comment:Wythagoras/FGH with transfinite ordinals/@comment-24509095-20140310142212

Isn't $$f_{\omega+1}(\omega)$$ equal to $$\varphi(1, 0, \omega)$$?

$$f_{\omega+1}(\omega)=f_\omega^\omega(\omega) = f_\omega(f_\omega(f_\omega(...f_\omega(f_\omega(\omega))...)))=f_\omega(f_\omega(f_\omega(...f_\omega(\varphi(\omega, 0))...)))=\varphi(\varphi(\varphi(\varphi(...\varphi(\omega, 0)..., 0), 0), 0), 0)$$

Correct me if I am wrong. I'm not good at using the Veblen function. :)