matrix function like iteration without power series expansion

[Gottfried]

Using a matrix-expression this would be

t°h(x) = W^-1 sum k=0..inf sum j=0..k (-1)^j * binomial(k,j) *diag(1,u^j,u^2j,...) * W

sum j=0..k (-1)^j * binomial(k,j) *dV(u^j) = diag(u^j-1) *PPow(
sum k=0..inf

what?

...editing-crap.

"not regularly" Euler-summable

However the aim was to not use the matrix method for computation.
This is faster and does not require the function to be developable into a powerseries.

Yes , sure - I only introduced the matrix-method to have an idea about the estimated coefficients.

I'm testing a summation-method, which allows to sum series of such rate of divergence. There are these Hausdorff-means, tightly related to the Riesz-method. Unfortunately it is not obvious, how - for a certain selection of parameters - the range of applicability can be determined. I'm comparing the results of my parameter-settings with known results for strongly diverging series and also I'm looking for articles on this...

Gottfried
z.B.:
Über Klassen von Limitierungsverfahren, die die Klasse der Hausdorffschen Verfahren als Spezialfall enthalten
Endl, Kurt
in: Mathematische Zeitschrift, volume: 65
pp. 113 - 132
Online at digicenter Göttingen