Re: " f^ [n](x) = exp( n/ phi' (x) D ) o x "

In article <1146765273.121843.263350@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<"alainverghote@xxxxxxxx"> wrote:

Dear Edgar ,

an other writing seems to be :
sum( k from 0 to infinity 1/ k! * { n / phi '(x) * d/dx } ^ k ) o
x .

What is that x on the end. A function? A variable?
If it is a variable, how do you compose with it?
Should the ending be " ... ^k)(x) " and not " ... ^k) o x " ??


I've tried the formula
exp( n/ phi' (x) D ) o x with a very simple
case f(x) = a*x +b , phi(x) =ln(x +b/(a-1)) / ln(a)
1 / phi'(x) = (x + b/(a -1) )*ln(a) .

I believe you 're right saying :
" a feeling it is a version
of the formula exp(aD)(g)(x) = g(x+a) which is a symbolic
way of writing the Taylor series. "

Amitiés , Alain


--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
.

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