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

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SUMMARY

The expression e^{e^{e^{x}}} does not simplify into a more manageable form or relate directly to hypergeometric functions. The notation is ambiguous without proper parentheses, and the standard right-to-left association does not yield simplification. The expression can be represented as a power series, specifically e^{e^{e^{x}}} = ∑_{n=0}^{∞} a_n x^n, where each coefficient a_n can be determined through further analysis.

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


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}
 


PlasticOh-No said:
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.
 


Thanks everyone for your help. Yes, I meant

e^{e^{e^{x}}}
 
Last edited:

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