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Can anyone identify this series? for n=1..infinity: e^((x^n)/n)

Posted on 2015-01-12
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Last Modified: 2015-01-12
so the series is

n=1: e^x
n=2: e^((x^2)/2)
n=3: e^((x^3)/3)
n=4: e^((x^4)/4)
n=5: e^((x^5)/5)
etc

Is there a method for finding the sum or the product of this series?
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Question by:purplesoup
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the product of the series would be
e^(x+(x^2)/2+(x^3)/3+(x^4)/4+(x^5)/5...)
=
e^(-log(1-x))   when  -1<=x<1
=
1/(1-x)

The sum of the series diverges.
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