Hello everybody.

My goal is to solve the following integro-functional equation:

(int(p^2/(f(p)-f(p+q)+omega), p = a .. b))/omega^2 = ln(omega^2+q^2)

(int(p^2/(f(p)-f(p+q)+omega), p = a .. b))/omega^2 = ln(omega^2+q^2)

where where is the unknown function and a, b are some numerical values as well as ω and q are real positive variables.

I would be grateful for any ideas.

Hello everybody.

I have a short question. I have an expression related to the calculation of the Gaussian curvature

-24.*y^6*(y-1.)^7*(y+1.)^7*(4.+6.*y^8-22.*y^6+30.*y^4-18.*y^2)/(4.*y^18-28.*y^16+84.*y^14+4.-136.*y^12+116.*y^10-24.*y^8-52.*y^6+56.*y^4-24.*y^2)^2

that is diverged for y=1 as (y-1)^(-2). 

At the same time substitution of something like y:=1.00001 gives the value almost zero. 

What is the trick?

Hello.

I would like to solve numerically highly nonlinear and cumbersome the second order differential equation. 

Applying the numerical procedure I got an error "Error, (in dsolve) found wrong extra argument(s): range = 0 .. 4*Pi, type = numerical". The similar problem has been described earlier here however I can't realize my problem. 

Below is my code

restart;

A1 := 8*Pi^3*R^2*n(x)^4*m+(2*Pi*sin((1/2)*x)*m*omega0*p+Pi*sin((1/2)*x)*m*omega0+3*Pi^2*(diff(n(x), x, x)))*n(x)^3+(-2*sin((1/2)*x)^2*m^2*omega0^2*p^2+2*cos((1/2)*x)^2*m^2*omega0^2*p^2-2*sin((1/2)*x)^2*m^2*omega0^2*p+2*cos((1/2)*x)^2*m^2*omega0^2*p)*n(x)^2+(-4*(diff(n(x), x, x))*sin((1/2)*x)^2*m^2*omega0^2*p^2-8*sin((1/2)*x)*(diff(n(x), x))*cos((1/2)*x)*m^2*omega0^2*p^2-4*(diff(n(x), x, x))*sin((1/2)*x)^2*m^2*omega0^2*p-8*sin((1/2)*x)*(diff(n(x), x))*cos((1/2)*x)*m^2*omega0^2*p)*n(x)+8*sin((1/2)*x)^2*(diff(n(x), x))^2*m^2*omega0^2*p^2+8*sin((1/2)*x)^2*(diff(n(x), x))^2*m^2*omega0^2*p;

R := 1; m := 1; p := 10; omega0 := 1000;

A2 := A1;

with(plots):
A3 := dsolve({A2, n(0) = n(4*Pi), (D(n))(0) = (D(n))(4*Pi)}, type = numerical, range = 0 .. 4*Pi):

odeplot(A3);

I appreciate for any help and suggestion.

Hello.

I'd like to extract numerical data from the plot of a implicit function and write it to the txt file. But, unfortunately due to a strong oscillating function and as a consequence extremely dense meshgrid I got a message that [Length of output exceeds limit of 1000000]. How to resolve this problem? Below is my code

restart;
R0 := 1+w_c*(sum((2*(-1)^(n+1)*Pi^2/n*n)*t*sin(2*Pi*n*mu/w_c)*cos(Pi*n)*exp(-2*Pi*n*G/w_c)/(w_c*sinh(2*Pi^2*n*t/w_c)), n = 1 .. 3000))/Pi-mu;
with(plots, implicitplot);
G := 0.; t := 0.1e-2;
R1 := implicitplot(R0, w_c = 0 .. 5, mu = 0 .. 3, gridrefine = 10):
data := getdata(R1);

Thank you in advance.

Good day.

I have a problem with the numerical approximation of incomplete elliptic integrals of the first kind in the case when the argument and the modulus are complex numbers. 

Let's consider an incomplete elliptic integral of the first kind EllipticF((a+I*b)*x, c+I*d), where a,b,c,d are arbitrary real numbers and x is very large number. Here is the code:

restart;
R0 := EllipticF((a+I*b)*x, c+I*d);
with(MultiSeries, series):
R1 := series(R0, x = infinity, 2);
a := .5; b := 1.75; c := 10; d := 12.5; x := 10^6;
evalf(R0); evalf(R1);

Below you can see that answers are different

.1680611942+.2058775337*I
-0.4563467782e-1-.3592094173*I+O(1/1000000000000000000)

While the same code for an incomplete elliptic integral of the second kind gives the correct approximation:

restart;
R00 := EllipticE((a+I*b)*x, c+I*d);
R11 := series(R00, x = infinity, 2);
a := .5; b := 1.75; c := 10; d := 12.5; x := 10^6;
evalf(R00); evalf(R11);
-1.687498740*10^7+2.374999011*10^7*I
-1.687501260*10^7+2.375000989*10^7*I+O(1/1000000)

What is the difference?