sumnumapinit

Function: sumnumapinit
Section: sums
C-Name: sumnumapinit
Prototype: DGp
Help: sumnumapinit({asymp}): initialize tables for Abel-Plana
 summation of a series.
Doc: initialize tables for Abel--Plana summation of a series $\sum f(n)$,
 where $f$ is holomorphic in a right half-plane.
 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
 ? sumnumap(n=1, n^-2);
 time = 163 ms.
 ? tab = sumnumapinit();
 time = 160 ms.
 ? sumnumap(n=1, n^-2, tab); \\ faster
 time = 7 ms.

 ? tab = sumnumapinit([+oo, log(2)]); \\ decrease like 2^-n
 time = 164 ms.
 ? sumnumap(n=1, 2^-n, tab) - 1
 time = 36 ms.
 %5 = 3.0127431466707723218 E-282

 ? tab = sumnumapinit([+oo, -4/3]); \\ decrease like n^(-4/3)
 time = 166 ms.
 ? sumnumap(n=1, n^(-4/3), tab);
 time = 181 ms.
 @eprog