(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.

**Follow-Ups**:**Re: (revision) NIntegrate that upper limit is infinite***From:*Daniel Lichtblau <danl@wolfram.com>