using sinh(x) ?

[tommy1729]

In principle a strategy is simple.

Show D^n ln(f(exp(x))) is close to D^n f(x) for all n > -1.

Write f(x) in the product form prod_i (1 + x^i / a_i) and use log(a b) = log a + log b.

So we get ( ignoring radius , continuation , summability ,...)

D^n F(x) ~~ D^n Sum_i ln( 1 + exp( i x) / a_i).

Use Taylor for ln(1 + x^t) and ln(x^3) = 3 ln(x) etc.

Should work.

In principle ... In theory ...

However in practice this is near impossible !?

See here at Gottfried's paper

http://go.helms-net.de/math/musings/drea...quence.pdf


Also posted on MSE by our friend Mick

http://math.stackexchange.com/questions/...of-lnfexpx



Regards

Tommy1729