216 Reputation

14 years, 255 days

Series substitution to find coefficients...

Maple
Dear All, I'm trying to substitute a series ansatz into a coupled couple of equations to find coefficients. The equations are quite cumbersome, but the principle shouldn't be too difficult. The equations are f3A(alpha,mu,Omega,delta,m) =0 f4A(alpha,mu,Omega,m) = 0 where f3A and f4A are complicated functions of the several variables. The region I'm working in is delta=0, m=1 Now, I have reason to believe that the following ansatz will work: alpha = A0 + A2/Omega^2 + A4/Omega^4 +.... -mu=M0 + M2/Omega^2 + M4/Omega^4 +.....

tensors for GR in maple...

Maple
Dear all, I'm trying to solve a difficult metric in maple. I did the following: restart; with(tensor): coords:=[t, r, theta,phi]: g:=array(symmetric,sparse,1..4,1..4): g[1,1]:=1+mu*a(r); g[2,2]:=-(1+mu*b(r)): g[3,3]:=-r^2*(1+mu*b(r)): g[4,4]:=-r^2*(sin(theta))^2*(1+mu*b(r)): g[4,1]:=mu*omega*f(r)*r^2*sin(theta)^2*(1+mu*b(r))/c: metric:=create([-1,-1], eval(g)); tensorsGR(coords,metric,contra_metric,det_met, C1, C2, Rm, Rc, R, G, C): display_allGR (coords,metric,contra_metric, det_met, C1, C2, Rm, Rc, R, G, C);

Asymptotic expansions of big integrals...

Maple
Dear All, I'm trying to make an asymptotic expansion of the following integral: A := m-> (x-sqrt(x^2+2*x*m+m^2-1))/(sqrt(x)*sqrt(x^2+2*x*m+m^2-1)) ; IntegralA := m-> evalf(Int(A(x, m), x = 0 .. infinity)) ; and similarly for two others P3 := m-> -(-1+4*x^2*m^2+8*x^3*m+2*x*m-3*x^2+m^2)/((2*x^2+1+2*sqrt((x+m)^2/((x+m+1)*(x+m-1)))*x^2)*(x+m+1)*(x+m-1)*sqrt(x)) ; IntegralP3:=m->evalf(Int(P3(x,m)/2,x=0..infinity)); and lastly P1:=(x,m)->sqrt(x)/(sqrt((x+m)^2-1)*(x+m+sqrt((x+m)^2-1))); IntegralP1:=m->evalf(Int(P1(x,1),x=0..infinity));

displaying 2-D & 3-D plots together...

Maple
Hello, Does anybody know if there's any way to display a 2-D plot & a 3-D plot on the same axes? I tried using display and I got the message: Error, (in plots:-display) cannot display 2-D and 3-D plots together Regards, Drew

Plotting a function which contains a (di...

Maple
Hello, This is related to my recent posts at http://www.mapleprimes.com/forum/integral-equations#comment-8339 I have a function of three variables one of which is inside a (difficult) integral. I want to calculate & store the array of points which satisfy the function, then use transform to change those points and then plot them. The function looks like this: P:=(x,m)->sqrt(x)/(sqrt((x+m)^2-1)*(x+m+sqrt((x+m)^2-1))); IntegralP:=(m)->Int(P(x,m),x=0..infinity); f4A:=(beta,Omega,m)->beta^2+(3*(beta*Omega)^(3/2)*evalf(IntegralP(m)))/(4*2^(3/4))-1; In my earlier case, m=1 (and there was another variable, but it wasn't under the integral) so the integral was not a problem. I tried the same method;
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