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MathGroup Archive 2006

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(revision) NIntegrate that upper limit is infinite

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71930] (revision) NIntegrate that upper limit is infinite
  • From: "Evanescence" <origine26 at yahoo.com.tw>
  • Date: Mon, 4 Dec 2006 06:39:12 -0500 (EST)

Dear all:
I am very sorry for my article contain a lot of mistake before.
So I check it and state my questions again.
I am really sorry that cause a lot of confuse for everybody.
My questions is as follows:
First I definite a function that is:
G[a_] := ((-(a -Cos[0.5])^(-3/2))/(3*(10)^2))*(Sin[0.5])^(2) +
(1/(1-0.1*0.1))*((0.005*(1 + Cos[0.5]) + 0.001/1000)*(1 +
Cos[0.5])^(1/2)*(ArcTan[(a - Cos[0.5])^(1/2)/(1 + Cos[0.5])^(1/2)] -
Pi/2) + (0.005*(1 - Cos[0.5]) - 0.001/1000)*(1 -
Cos[0.5])^(1/2)*(ArcTanh[(1 - Cos[0.5])^(1/2)/(a - Cos[0.5])^(1/2)]))

another function is:
P[a_]:=Re[N[LegendreP[(-1/2)+I,a]]]       where I=(-1)^(1/2)

then
NIntegrate[G[a]*P[a], {a, 1, Infinity}]

but get error message is:
NIntegrate's singularity handling has failed at point
{a}={2.7013362243395366*(10^150)}for the specified
precision goal.
Try using larger values for any of $MaxExtraPrecision
or the options WorkingPrecision, or SingularityDepth and MaxRecursion.

NIntegrate::"inum":
"Integrand G[a]*P[a] is not numerical at {a}=
{2.7013362243395366`*(10^150)}.

Please solve my confuse ,thank you very much!

By the way
G[Infinity]*P[Infinity]=0 ¡A G[1] is singular point¡AP[1]=1
and I try Plot the graph for G[a]¡AP[a]¡Aand G[a]*P[a] ¡Afrom the
graph of  G[a]*P[a] 
it should convergence for a-->Infinity.


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