sumnummonien

Function: sumnummonien
Section: sums
C-Name: sumnummonien0
Prototype: V=GEDGp
Help: sumnummonien(n=a,f,{tab}): numerical summation from
 n = a to +infinity using Monien summation.
Wrapper: (,G)
Description:
  (gen,gen,?gen):gen:prec sumnummonien(${2 cookie}, ${2 wrapper}, $1, $3, $prec)
Doc: numerical summation $\sum_{n\geq a} f(n)$ at high accuracy, the variable
 $n$ taking values from the integer $a$ to $+\infty$ using Monien summation,
 which assumes that $f(1/z)$ has a complex analytic continuation in a (complex)
 neighbourhood of the segment $[0,1]$.

 The function $f$ is evaluated at $O(D / \log D)$ real arguments,
 where $D \approx \kbd{realprecision} \cdot \log(10)$.
 By default, assume that $f(n) = O(n^{-2})$ and has a nonzero asymptotic
 expansion
 $$f(n) = \sum_{i\geq 2} a_i n^{-i}$$
 at infinity. To handle more complicated behaviors and allow time-saving
 precomputations (for a given \kbd{realprecision}), see \kbd{sumnummonieninit}.