User blog comment:Simplicityaboveall/Extremely Large Numbers 4/@comment-5529393-20160801195700/@comment-24920136-20160803023311

Yes but that is a custom function of Chris Bird, it is not standard nor canonical

he says in line 21 of that document you linked:

"I have redefined Knuth’s Up-arrow Notation with transfinite values so"

As you can see that is his original work and not standard math