intcirc

Function: intcirc
Section: sums
C-Name: intcirc0
Prototype: V=GGEDGp
Help: intcirc(X=a,R,expr,{tab}): numerical integration of expr on the circle
 |z-a|=R, divided by 2*I*Pi. tab is as in intnum.
Wrapper: (,,G)
Description:
  (gen,gen,gen,?gen):gen:prec intcirc(${3 cookie}, ${3 wrapper}, $1, $2, $4, $prec)
Doc: numerical
 integration of $(2i\pi)^{-1}\var{expr}$ with respect to $X$ on the circle
 $|X-a| = R$.
 In other words, when \var{expr} is a meromorphic
 function, sum of the residues in the corresponding disk; \var{tab} is as in
 \kbd{intnum}, except that if computed with \kbd{intnuminit} it should be with
 the endpoints \kbd{[-1, 1]}.

 \bprog
 ? \p105
 ? intcirc(s=1, 0.5, zeta(s)) - 1
 time = 496 ms.
 %1 = 1.2883911040127271720 E-101 + 0.E-118*I
 @eprog

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