Sumaia Saad-Eddin on Mon, 18 Oct 2010 15:54:57 +0200

 Integration

```Dear all,

here is a simple script I use:
----------------------------------------------------
{calF3b(n, y, borne=0)=
local(res);
if(borne == 0,
res = intnum(u = y, [[1], I],
(n*(n-1)*log(u/y)^(n-2)
-n*log(u/y)^(n-1)
+2*(-n*log(u/y)^(n-1)+log(u/y)^n))*(-cos(u))/u^3
)*2/factorial(n),
res = intnum(u = y, borne,
(n*(n-1)*log(u/y)^(n-2)
-n*log(u/y)^(n-1)
+2*(-n*log(u/y)^(n-1)+log(u/y)^n))*(-cos(u))/u^3
)*2/factorial(n));
return(res);
}
-------------------------------------------------
And then:
------------------------------------------------
? default(realprecision, 200);
? calF3b(3, 5, 0)
%24 =
-0.0014856416479696953928448903497326047373162140908013809557457050551373320878332013935070207158553203686531222066372995251233206569487841668099460986174588469189370065932422491349757424944029721562740578
? calF3b(3, 5, 1000)
%25 =
-0.0014856627355888837790517373518799598562592890176944537692015849210748454162194856065031296971028332780195925404567414258318215629128028619431494341708703232462104962505815455183302302207438155760827252
? calF3b(3, 5, 10000)
%26 =
-0.0014797277179347064177532972573409986024162997470900911555361077225939621992399038808681398516168186547356007049683292650261103144255778980107135555010306584599354594552108552028831561946152770233217702
? calF3b(3, 5, 100000)
%27 =
-0.0014923749632841228130828117074689824573212046115472117963604716758907190884104283414505365906272331638082132284475597672118202238948186809803203022515326726288826288931730256153115499066993338887350605
----------------------------------------------

Can anyone explain me why these results are so
different, or give me a pointer to some litterature?