Taylor series of upx function

[Kouznetsov]

Well I cannot deduce your expression.

My expression is
\( \ln(f'(x))=f'(-1)-f'(0)+f(x-1) + \ln(f'(x-1)) \)
It can be deduced in the following way:
\(
\ln\left( f'(x) \right) =
\ln\left( \frac{{\rm d}}{{\rm d} x} f(x) \right) =
\ln\left( \frac{{\rm d}}{{\rm d} x} \exp(f(x-1)) \right) =
\ln\left( \exp(f(x-1)) \cdot f'(x-1) \right) =
\ln\Big( \exp(f(x-1)) \Big) + \ln\Big( f'(x-1) \Big) =
f(x-1)+ \ln\Big( f'(x-1) \Big) =
f(x-1)+ \ln\Big( f'(x-1) \Big) + f'(-1)-f'(0)
\)
,
because \( f'(-1)=f'(0) \).

I meant sexp with natural base. What I can derive is:
\(
\ln \frac{f'(x)}{f'(0)} = f(0)+...+f(x-1)
\)

What is sense of ... in this expression?
How does Ansus get this espressionan?