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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)}.
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