Re: About NIntegrate
- 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