@tomleslie 

Thank you so much, now I got the point

@tomleslie 

Thank you so much for your helpful reply.

Even for j=1, lets say red colour curve, there are two curves there, How can I get rid of one of it?

@acer  Thanks a lot,

now its solved I think.

@acer it should be,

d := z -> t*d__sc/(1-z)

@tomleslie 

Above suggestions were really very constructive and thus helpful.

Further, how can I add two such plots together,

lets say'I wish to have two plots together with different values of $x$, such as $x=0$  and $x=0.3$, values of other parameters remain same ($a=0.5$, $s=1$).

@tomleslie

Please see the file attached.

I need a plot of $alpha$ with $a=0.5,x=0.8, s=+1$.

Yes I think I should first pick the range where this function is well behaved.

Right?

Kindly help. The previous mail was really helpful.

 KSBH-Deflection-Angle-IMP.mw

@tomleslie

> restart;
> M := -a+2*sqrt(3*(3-x))*cos((1/3)*arccos(-3*a*sqrt(3/(3-x))/(3-x)));
> b := M/(1-B);
> 
> r := 2*sqrt(b^2-a^2-(1/3)*x^2)*cos((1/3)*arccos(-(3*((1/2)*sqrt(3)))*(2*(b-a)^2-1/27*(9*x*(b^2-a^2)+2*x^3))/(b^2-a^2-(1/3)*x^2)^(3/2)))/sqrt(3)+(1/3)*x;
> h := 1/r;
> w[s] := a/b;
> h[sc] := (b+a)/(b-a);
> H := 1-3*(b+a)/(r*(b-a));
> k := 1/2-(1-6*H/h[sc])/(2*((h[sc]-2*H)*(h[sc]+6*H)+8*x^2/(b^2*(1-w[s])^2))^(1/2)/h[sc]);

> n := (1-6*H/h[sc]+2*((h[sc]-2*H)*(h[sc]+6*H)+8*x^2/(b^2*(1-w[s])^2))^(1/2)/h[sc])/(1-2*H/h[sc]-(2*(2+x))/(h[sc]*(2*x+a^2))+2*((h[sc]-2*H)*(h[sc]+6*H)+8*x^2/(b^2*(1-w[s])^2))^(1/2)/h[sc]+sqrt((2+x)^2-4*(2*x+a^2))/(h[sc]*(2*x+a^2)));

I want a plot of EllipticPi(n,k) @ a=0.5 and x=0.8 with B=0..1.

Is there a way to simplify the expressions?

@Markiyan Hirnyk 

Thank You So much

@Markiyan Hirnyk 

Is it possible to use the obtained dataset for algebric calculations directly? Such as how can I calculate (Column#1)^2-\sqrt{(Column#2)^2-(Column#3)^2}

@Markiyan Hirnyk 

Thanks a lot

@Preben Alsholm 

Thanks for your reply, it was very helpful

@Markiyan Hirnyk 

Thank you so much,

it is helpful

@Markiyan Hirnyk 

Is it just about the ranges of the variables included?

@Markiyan Hirnyk 

Thanks for your response.

By 3d polarplot I mean spherical polar system. If I have three first order differential equations for variables r(t), theta(t), phi(t) (where theta and phi are angles). Then I need a solution of the set of diff eqs in form of a plot, wjere the range $theta=0 ..2*Pi$ & $Phi=0 .. 2*Pi$.

The previously given set of diff eq. can also be taken into account, where w[2] and w[3] will then be angles and w[1] will refer to the radial co-ordinate.

@ecterrab 

I'm using Maple 12,

I want to find out raychaudhuri equations for arbitrary metric which are evolution equations for expension, shear and vorticity parameters of geodesic congruences.