• To: mathgroup at smc.vnet.net
• Subject: [mg71418] Re: About NIntegrate
• From: "Evanescence" <origine26 at yahoo.com.tw>
• Date: Fri, 17 Nov 2006 04:30:54 -0500 (EST)
• References: <ejf0mv\$3qv\$1@smc.vnet.net><ejgvdu\$8q5\$1@smc.vnet.net>

```Jean-Marc Gulliet ¼g¹D¡G

> Evanescence wrote:
> > Dear all: My question is as follows:
> >
> > First I definite one variable is: a=Cosh[b]
> > then,I definite two functions:
> > one is :
> > P[a_]=(((2)^(1/2))/Pi)*Integrate[(Cosh[I*t])/((a-Cosh[t])^^(1/2)),0,b,t]
First¡Avery thank you Mr. Jean-Marc answers very question.
Actually¡Awhen I key in above function P[a_]¡A I use the
Palettes-BasicInput in Mathematica
the  wrong syntax was caused only in here that i do not notice ,sorry!

> Wrong syntax here------------------------------------------!!andhere!!!!
> Must be
>
> In[1]:=
> a = Cosh[b];
> P[a_] = (2^(1/2)/Pi)*Integrate[Cosh[I*t]/
>       (a - Cosh[t])^(1/2), {t, 0, b}]
>
> Out[2]=
>                            Cos[t]
> Sqrt[2] Integrate[-----------------------, {t, 0, b}]
>                    Sqrt[Cosh[b] - Cosh[t]]
> -----------------------------------------------------
>                           Pi
>
> >   ! (I is the (-1)^(1/2)) ,the upper limit is b, the lower limit is 0)
> > another
> > is:G[a_]=((-(a-Cos[0.5])^(-3/2))/(3*(10)^2))*(Sin[0.5])^(2)+(1/1-0.5*0.1)*((0.025*(1+Cos[0.5])+0.4/999)*(1+Cos[0.5])^(1/2)*(ArcTan[(a-Cos[0.5])^(1/2)/(1+Cos[0.5])^(1/2)]-Pi/2)+(0.025*(1-Cos[0.5])-0.4/999)*(1+Cos[0.5])^(1/2)*(ArcTanh[(1-Cos[0.5])^(1/2)/(a-Cos[0.5])^(1/2)])
> Missing parentheses. Should be
>
> In[3]:=
> G[a_] = (-(a - Cos[0.5])^(-3/2)/(3*10^2))*Sin[0.5]^2 +
>     (1/1 - 0.5*0.1)*(0.025*(1 + Cos[0.5]) + 0.4/999)*
>      (1 + Cos[0.5])^(1/2)*
>      (ArcTan[(a - Cos[0.5])^(1/2)/(1 + Cos[0.5])^
>          (1/2)] - Pi/2) + (0.025*(1 - Cos[0.5]) -
>       0.4/999)*(1 + Cos[0.5])^(1/2)*
>      ArcTanh[(1 - Cos[0.5])^(1/2)/(a - Cos[0.5])^(1/2)]
>
> Out[3]=
>               Pi
> 0.0616242 (-(--) + ArcTan[0.729794 Sqrt[-0.877583 + Cosh[b]]]) +
>               2
>
>                               0.349882
>    0.00364491 ArcTanh[-------------------------] -
>                       Sqrt[-0.877583 + Cosh[b]]
>
>          0.000766163
>    ------------------------
>                         3/2
>    (-0.877583 + Cosh[b])
>
>
> > then
> > NIntegrate[P[a]*G[a],{a,1,Infinity}]
> > but get error message is NIntegrate P[a]*G[a] is not numerical at
> > {a}={2.}
>
> The variable b does not seem to have any value. Did you mean something like
>
> NIntegrate[P[b]*G[b], {b, 1, Infinity}]
>
Actually the P[a] is the function of LegendreP¡A P[a] is it's
definition
So that the P[a] is the function of a
a = Cosh[b] ==>b=ArcCosh[a]
P[a_] = (2^(1/2)/Pi)*Integrate[Cosh[I*t]/(a - Cosh[t])^(1/2), {t, 0,
b}]==> so the integrate result is function of a
b does not have any value because b=ArcCosh[a] and b is the upper
limit.
so the NIntegrate[P[a]*G[a],{a,1,Infinity}] seem to can NIntegrate ,but
I get error message as above.
By the way , my English is not good ,so very statement is not detailed
and well  please pardon me ^^"

Regards,
Evanescence.

> Regards,
> Jean-Marc

```

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