Function: suminf
Section: sums
C-Name: suminf0
Prototype: V=GEp
Help: suminf(X=a,expr): infinite sum (X goes from a to infinity) of real or
 complex expression expr.
Wrapper: (,G)
Description:
  (gen,gen):gen:prec suminf(${2 cookie}, ${2 wrapper}, $1, $prec)
Doc: \idx{infinite sum} of expression
 \var{expr}, the formal parameter $X$ starting at $a$. The evaluation stops
 when the relative error of the expression is less than the default precision
 for 3 consecutive evaluations. The expressions must always evaluate to a
 complex number.

 If the series converges slowly, make sure \kbd{realprecision} is low (even 28
 digits may be too much). In this case, if the series is alternating or the
 terms have a constant sign, \tet{sumalt} and \tet{sumpos} should be used
 instead.

 \bprog
 ? \p28
 ? suminf(i = 1, -(-1)^i / i)   \\@com Had to hit \kbd{C-C}
   ***   at top-level: suminf(i=1,-(-1)^i/i)
   ***                                ^------
   *** suminf: user interrupt after 10min, 20,100 ms.
 ? sumalt(i = 1, -(-1)^i / i) - log(2)
 time = 0 ms.
 %1 = -2.524354897 E-29
 @eprog

 \synt{suminf}{void *E, GEN (*eval)(void*,GEN), GEN a, long prec}.
