N function problematic performance (V. 5.2)

• To: mathgroup at smc.vnet.net
• Subject: [mg74757] N function problematic performance (V. 5.2)
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Wed, 4 Apr 2007 04:02:19 -0400 (EDT)

```Consider the following the definite integral

h = HoldForm[Integrate[Sin[x - 1]/Sqrt[x*(x - 2)], {x, 2, Infinity}]]

Here is a numerical estimation

ReleaseHold[h /. Integrate[x___] :> NIntegrate[x, Method ->
Oscillatory]]
1.2019697137297456

Here is the symbolic result by Mathematica

Timing[hh = ReleaseHold[h]]

{30.031000000000002*Second, (Pi*(Cos[1]*MeijerG[{{}, {1/4, 3/4}}, {{0,
1/2, 1/2}, {0}}, 1] -
MeijerG[{{}, {1/4, 3/4}}, {{0, 0, 1/2}, {1/2}}, 1]*Sin[1]))/
Sqrt[2]}

Application of N function results in unexpected warnings and not in
any estimation in reasonable timing...

TimeConstrained[N[hh], 120]
Infinity::"indet"...
NSum::nsnum :...
\$Aborted

What is going here?
Did I encouter a known (problematic) situation?

BTW,

Integrate[TrigToExp[Sin[x - 1]/Sqrt[x*(x - 2)]], {x, 2, Infinity}]
((1/2)*I*Pi^(3/2)*(E^(2*I)*MeijerG[{{}, {1/2, 1/2}}, {{0, 0}, {1/2}},
-2*I] - MeijerG[{{}, {1/2, 1/2}}, {{0, 0}, {1/2}}, 2*I]))/
E^I

Chop[N[%]]
-1.2019697153172064

which is opposite of the correct result.

```

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