An asnwer in the newsgroup sci.math:
Dear Gottfried,
the function tf(x) verifies
exp(tf(x)) + exp(x) = 2*x +2
So
tf(x)=ln( -exp(x) +2*x+2)
and series near 0,
x - x^2 + 2/3x^3 - 3/4 x^4 + 11/15 x^5 ... [I corrected a missing term]
Alain
So I took the long way...
Gottfried
Dear Gottfried,
the function tf(x) verifies
exp(tf(x)) + exp(x) = 2*x +2
So
tf(x)=ln( -exp(x) +2*x+2)
and series near 0,
x - x^2 + 2/3x^3 - 3/4 x^4 + 11/15 x^5 ... [I corrected a missing term]
Alain
So I took the long way...
Gottfried
Gottfried Helms, Kassel