ln(1+exp(a.x)) expression ?

[fordsp]

hi all,

are there any one who come accross such an expression:

ln(1+e^(a.x))

I need a serial representation (polynomial form) of it. It is going to be used
in an optimizatiton problem based on x (x is not able to be ignored, whole expression is required).
I would really appriciate if one gives a response soon...thanks,

Regards.

 

[LouisSheffield]

Please clarify what you mean by a.x

 

[o_0]

I think that the dot means multiplication as in "a multiplied by x"

Anyway back to the question, to figure out the series follow this tutorial on Taylor/Maclaurin series: Pauls Online Notes : Calculus II - Taylor Series

 

[_Eduardo_]

Just enter ln(1+e^(a x)) in WolframAlpha

 

[fordsp]

Just enter ln(1+e^(a x)) in WolframAlpha

thanks all,
I used the result (series expansion) documented in "WolframAlpha"...it works...thanks in advance,
regards...

 

[LouisSheffield]

Be very careful to bound ax. Depending on how many terms you retain, somewhere in the interval 3 < |ax| < 4 the various terms will begin to oscillate and then diverge.

 

[_Eduardo_]

The convergence radius is pi.
That is: |ax| < 3.14..