Function: sumnuminit
Section: sums
C-Name: sumnuminit
Prototype: DGp
Help: sumnuminit({asymp}): initialize tables for Euler-MacLaurin delta
 summation of a series with positive terms.
Doc: initialize tables for Euler--MacLaurin delta summation of a series with
 positive terms. If given, \kbd{asymp} is of the form $[\kbd{+oo}, \alpha]$,
 as in \tet{intnum} and indicates the decrease rate at infinity of functions
 to be summed. A positive
 $\alpha > 0$ encodes an exponential decrease of type $\exp(-\alpha n)$ and
 a negative $-2 < \alpha < -1$ encodes a slow polynomial decrease of type
 $n^{\alpha}$.
 \bprog
 ? \p200
 ? sumnum(n=1, n^-2);
 time = 200 ms.
 ? tab = sumnuminit();
 time = 188 ms.
 ? sumnum(n=1, n^-2, tab); \\ faster
 time = 8 ms.

 ? tab = sumnuminit([+oo, log(2)]); \\ decrease like 2^-n
 time = 200 ms.
 ? sumnum(n=1, 2^-n, tab)
 time = 44 ms.

 ? tab = sumnuminit([+oo, -4/3]); \\ decrease like n^(-4/3)
 time = 200 ms.
 ? sumnum(n=1, n^(-4/3), tab);
 time = 221 ms.
 @eprog
