After conversion to LegendreP (and even before separating real and imaginary parts, and with symbolic epsilon assumed nonnegative) does it not fall out that the given integrand is symmetric about theta=Pi/2?

I mean, is this incorrect? (say invalid in the limit...)

restart;
chi:=Pi/2-theta:

Vsi:=-(1/sqrt( 1+epsilon - cos(chi)*cos(phi-Pi/3))
     + 1/sqrt( 1 +epsilon- cos(chi)*cos(phi-Pi))
     + 1/sqrt(1+epsilon-cos(chi)*cos(phi+Pi/3))):

igrand:=Vsi*SphericalY(3,2,theta,phi)
        *conjugate(SphericalY(2,1,theta,phi))*sin(theta):

simplify(convert(igrand-eval(igrand,theta=Pi-theta),LegendreP))
     assuming theta>=0, theta<=Pi, phi>=0, phi<=2*Pi, epsilon>=0;

                               0

acer

@Carl Love main menubar Edit -> Startup Code (Ctrl-Shift-E on MS-Win)

That procedure in that worksheet is defined in the Startup Code.

@Carl Love main menubar Edit -> Startup Code (Ctrl-Shift-E on MS-Win)

That procedure in that worksheet is defined in the Startup Code.

@wzelik So, is it the case that now you want to utilise the values assigned to solT4, solT3, and solT2 inside eqT3, eqT2, and eqT1 respectively?

Something like this, perhaps?

   eqT3 := (Tin-T3)*A/(1/hin+g1/lambda1+g2/lambda2) = (T3-solT4)*A*lambda3/g3;
   solT3 := fsolve(eqT3,T3=0..2000);

   eqT2 := (Tin-T2)*A/(1/hin+g1/lambda1) = (T2-solT3)*A*lambda2/g2;
   solT2 := fsolve(eqT2, T2=0..2000);

   eqT1 := (Tin-T1)*A*hin = (T1-solT2)*A*lambda1/g1;
   solT1 := fsolve(eqT1,T1=0..2000);   

I'm not sure whether you goal is to just experiment with embedded components, or to build a final version of some application of your own devising. If it's the latter case then you might want to note that you can isolate the unknown T2 in eqT2, etc. By isolating just once, in advance, you might obtain reusable formulae and so avoid reliance on fsolve (for some particular equations of this example).

@wzelik So, is it the case that now you want to utilise the values assigned to solT4, solT3, and solT2 inside eqT3, eqT2, and eqT1 respectively?

Something like this, perhaps?

   eqT3 := (Tin-T3)*A/(1/hin+g1/lambda1+g2/lambda2) = (T3-solT4)*A*lambda3/g3;
   solT3 := fsolve(eqT3,T3=0..2000);

   eqT2 := (Tin-T2)*A/(1/hin+g1/lambda1) = (T2-solT3)*A*lambda2/g2;
   solT2 := fsolve(eqT2, T2=0..2000);

   eqT1 := (Tin-T1)*A*hin = (T1-solT2)*A*lambda1/g1;
   solT1 := fsolve(eqT1,T1=0..2000);   

I'm not sure whether you goal is to just experiment with embedded components, or to build a final version of some application of your own devising. If it's the latter case then you might want to note that you can isolate the unknown T2 in eqT2, etc. By isolating just once, in advance, you might obtain reusable formulae and so avoid reliance on fsolve (for some particular equations of this example).

@mehdi_mech How can we tell whether your system is stiff, or poorly scaled, or intrinsically difficult, etc, if you do not show it in full or upload it in this thread?

I cannot know in advance whether stiff methods might help for a problem unseen, but enabling them is described on the help pages of dsolve,numeric.

Are you forcing a method, such as rkf45? If that is so, then why? Could the problem be stiff?

acer

Why don't you upload a worksheet with the problematic examples in it?

acer

@TI_ET_User I'm sorry, I had it wrongly fixed in my mind that you were discussing something which did pretty much the opposite. Please ignore my earlier comments.

@TI_ET_User I'm sorry, I had it wrongly fixed in my mind that you were discussing something which did pretty much the opposite. Please ignore my earlier comments.

I have 32bit Maple 11.02 working on 64bit Windows 7 Pro. The File-Open menu item appears to work ok.

Wasn't there an update (11.02?) that allowed it to work with Vista? Is that possibly related here? But that download is not longer available via the support area of the website. Does "Check for Updates" indicate anything, if run from the menubar under the Tools menu item?

Apparently I'm not the only one who got it to work.

acer

I have 32bit Maple 11.02 working on 64bit Windows 7 Pro. The File-Open menu item appears to work ok.

Wasn't there an update (11.02?) that allowed it to work with Vista? Is that possibly related here? But that download is not longer available via the support area of the website. Does "Check for Updates" indicate anything, if run from the menubar under the Tools menu item?

Apparently I'm not the only one who got it to work.

acer

There was a time when `NextZero` wasn't so powerful (or was a little more buggy). But perhaps it's time for its functionality to be rolled into fsolve (connected to the `maxsols` option, perhaps?).

I once tried to roll it into a slightly easier-to-use procedure. The main bit about it which wasn't just candy was that it tried to handle and adjust the search range for itself.

acer

There was a time when `NextZero` wasn't so powerful (or was a little more buggy). But perhaps it's time for its functionality to be rolled into fsolve (connected to the `maxsols` option, perhaps?).

I once tried to roll it into a slightly easier-to-use procedure. The main bit about it which wasn't just candy was that it tried to handle and adjust the search range for itself.

acer

@marc005 

In your original: "What is the probability that the other is a girl?"

In your stock example: "What is the probability that stock 2 has a positive return?"

In the original, it is not given which is the boy. So the identity of the "other" is not specified. In contrast, in the stock example you specifically ask about stock 2.