       help in Numerical Intergation

• To: mathgroup at smc.vnet.net
• Subject: [mg36518] help in Numerical Intergation
• From: "Salman Durrani" <dsalman at itee.uq.edu.au>
• Date: Tue, 10 Sep 2002 06:24:52 -0400 (EDT)
• Organization: The University of Queensland, Australia
• Sender: owner-wri-mathgroup at wolfram.com

```Hi

I am having some trouble with numerical integration.

\!\(\(\(Timing[
ansOUT = {}; \[IndentingNewLine]For[EbNo = 0, EbNo <= 2,
EbNo += 10\/10, \[IndentingNewLine]linEbNo =
10\^\(EbNo\/10\); \[IndentingNewLine]M = 64; \[IndentingNewLine]K =
Log[2, M]; \[IndentingNewLine]p = \(M/2\)\/\(M - 1\)\ Sum[
Binomial[M - 1,
n] \((\(-1\))\)\^\(n + 1\)\/\(1 + n\)\ Exp[\(-\
linEbNo\)\ K\ n\/\(1 + n\)], {n, 1,
M - 1}]; \[IndentingNewLine]Pm = \(1\/\@\(2\ \[Pi]\)\)
NIntegrate[
1 - \(\((\(1\/\@\(2\ \[Pi]\)\)
NIntegrate[
Exp[\(-x\^2\)\/2], {x, \(-\[Infinity]\), y},
WorkingPrecision -> 32\ ])\)\^\(M - 1\)\)
Exp[\(\(-1\)\/2\) \((y - \@\(2\ K\ linEbNo\))\)\^2], {y,
\(-\
\[Infinity]\), \[Infinity]},
WorkingPrecision ->
32]; \[IndentingNewLine]Pb = \(\(M/2\)\/\(M - 1\)\)
Pm; \[IndentingNewLine]AppendTo[
ansOUT, {N[a, 4], N[p, 8],
N[Pb, 8]}];\[IndentingNewLine]];]\)\(\[IndentingNewLine]\)\)\)
TableForm[ansOUT]

The code can also be downloaded from

Col. 2(symblic formula) and 3 (result of numerical integration) of the
variable ansOUT should be identical.

However the numerical integration is giving a 0 answer.

Can anyone please suggest how a solution to this problem.

Thanks

Salman

```

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