Rearranging exponential functionsUsing two different strategies, I've derived an equation for a particular function f ( ϕ ). That equation is f ( ϕ ) = 1 1 − e − T γ ( 1 − e − T γ ϕ ) .However, the paper whose result I'm trying to replicate is telling me that the function is f ( ϕ ) = ( 1 − e − γ ) ( 1 − e − γ ϕ ) .Is there a way to rearrange the result I got so that it matches the result in the paper?EDIT:What's confusing me about this is that the function needs to be such that f ( 0 ) = 0 and f ( 1 ) = 1. This is true of the equation I derived. But for the equation in the paper, f ( 1 ) = 1 only if γ = ln ⁡ ( 1 / 2 ), which is not the case in the specific example given later in the paper. So something weird is afoot (either on my part or on the paper's).

Question

Rearranging exponential functionsUsing two different strategies, I&#039;ve derived an equation for a particular function   f  (  ϕ  ). That equation is  f  (  ϕ  )  =      1          1      −              e                  −          T          γ                      (  1  −      e          −      T      γ      ϕ        )  .However, the paper whose result I&#039;m trying to replicate is telling me that the function is  f  (  ϕ  )  =  (  1  −      e          −      γ        )  (  1  −      e          −      γ      ϕ        )  .Is there a way to rearrange the result I got so that it matches the result in the paper?EDIT:What&#039;s confusing me about this is that the function needs to be such that   f  (  0  )  =  0 and   f  (  1  )  =  1. This is true of the equation I derived. But for the equation in the paper,   f  (  1  )  =  1 only if   γ  =  ln  ⁡  (  1      /    2  ), which is not the case in the specific example given later in the paper. So something weird is afoot (either on my part or on the paper&#039;s).

conveneau71 · Accepted Answer

The functions are not the same. My test: set each variable to 3 (  γ  =  3  ,  ϕ  =  3  ,  T  =  3) and evaluate. Your function evaluates to   f  (  3  )  =  1.000123425. The paper&#039;s function evaluates to   f  (  3  )  =  0.950095666.

Rearranging exponential functions Using two different strategies, I've derived an equation for a pa

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