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