Re: NIntegrate that upper limit is infinite

*To*: mathgroup at smc.vnet.net*Subject*: [mg71923] Re: NIntegrate that upper limit is infinite*From*: "Evanescence" <origine26 at yahoo.com.tw>*Date*: Mon, 4 Dec 2006 06:38:49 -0500 (EST)*References*: <ekp4q1$2h9$1@smc.vnet.net><ekrjk2$ri4$1@smc.vnet.net>

Jean-Marc Gulliet ¼g¹D¡G > Evanescence wrote: > > Dear all: > > My question 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)]) > -------^ [1] > --------------------------------------------------------------------------------------------^ > [2] > [1] SetDelayed, that is :=, for function definition is better. > [2] Missing parenthesis > > So, the correct expression 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) > -------^ [3] -----------------^ [4] > [3] SetDelayed, that is :=, for function definition is better. > [4] Sqrt[-1] is written capital I in Mathematica. > > Therefore, the correct expression is > > P[a_] := Re[N[LegendreP[-2^(-1) + I, a]]] > > > then > > NIntegrate[G[a]*P[a],{a,1,infinite}] > ----------------------------^^^^^^^^ [5] > [5] Positive infinity is written Infinity in Mathematica. > > Hence, the correct expression is > > NIntegrate[G[a]*P[a], {a, 1, Infinity}] > > > but get the error message > ----------^^^ > Which one did you get? There are dozens of possible messages... > > Regards, > Jean-Marc First very thank you Mr. Jean-Marc answers very question. About your suggestion [1] and [3] I think you are right,thank you About [4] and [5] ,actually I use the Palettes-BasicInput in Mathematica ,the wrong syntax was caused only in here that i do not notice ,sorry! The error message which I get is as follows: NIntegrate::singd : 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)}.