Talk:Padé approximant

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The epsilon algorithm, the page refers to for getting the coefficients is missing. A search leads to nothing. I'm not from that field and thus cannot contribute the missing page. 84.226.41.90 17:52, 21 January 2007 (UTC)

[edit] Riemann-Padé Zeta function

(EDIT)

To study the resummation of divergent series, it can be useful to introduce the Padé o simply Rational zeta function as:

\sum_{n=1}^{\infty} \frac{[N/M]_f(n)}{n^{s}}= \zeta _{Q}(s)

so the zeta regularization value at s=0 it is equal to the 'sum' S, of the divergent series:

S= \sum_{n=1}^{\infty}f(n)

the functional equation for this Pade zeta as:

\sum_{j=0}^{M}p_{j}\zeta _{Q}(s-j)= \sum_{j=0}^{N}q_{j}\zeta_{0}(s-j)

here '0' means that the Pade is of order [0/0] and hence, we got the Riemann zeta function. and Q = Q(n) = [N / M]f(n)

Sorry.. for my edition, perhaps now it looks clearer from the coefficients of the upper and lower Polynomials involving Padè approximant (If possible put it back) i thought i saw it into a book about Dirichlet series but can not remember its name.

The above section appeared in the article. It looks to me as it is valid, but unfortunately I have no idea what's meant. In the first formula, the numerator seems to be independent of n; and what is Q? In the last formula, the a_j and b_j is not defined. -- Jitse Niesen (talk) 13:28, 23 October 2007 (UTC)

Okay, it looks clearer now; thanks. I changed it a bit, hopefully without introducing any errors. -- Jitse Niesen (talk) 11:45, 26 October 2007 (UTC)