Can e^{e^{e^{x}}} Be Simplified or Related to Hypergeometric Functions?

[PlasticOh-No]

Is there any way to simplify or clarify e^e^e^x ?
Some sort of equivalence to a hypergeometric?
How about e^e^x?
Thanks

 

[CRGreathouse]

Assuming that these associate the usual way (right-to-left), they don't really simplify.

 

[HallsofIvy]

What you have written, without parentheses,is ambiguous. That is why CRGreathouse said "Assuming that these associate the usual way (right-to-left)".

e^{e^{e^x}}
does not simplify.

((e^e)^e)^x= (e^e)^{ex}= e^{e^2x}

 

[jackmell]

Is there any way to simplify or clarify e^e^e^x ?
Some sort of equivalence to a hypergeometric?
How about e^e^x?
Thanks

Assume it's the way I think you want it to be:

e^{e^{e^{x}}}=\sum_{n=0}^{\infty} a_n x^n

and you know how to figure out what each a_n is.

 

[PlasticOh-No]

Thanks everyone for your help. Yes, I meant

e^{e^{e^{x}}}