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These are replies submitted by Vortex

@Preben Alsholm 

Thank you fo the answer and for the suggestion. Here for this differential equation a parameter p is an ineteger number. At least for p=0 there is an analytical solution expressed in terms of periodic functions, namely sine and cosine fucntions. So obviously based on that periodic conditions I expect to obtain periodic solutuion also.

I have tried already to use initial function as sin(x)+cos(x) but now I experience another problem "Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging".

@nm Many thank for the reply and for the improvment! It's just my unwanted error with the incorrect call of the type for the solution.

I have chosen n(x) as a function for the convinience to export later this expression to latex. 


Thank you for the comment and for the help. I found the solution (see my comment above).

@Preben Alsholm 

It's ok. I have resolved that issue and I have extracted the data.

Thanks a lot for the reply.

I know that the execution of the code is rather long but my problem is that I can't extract the data file from the plot due to this warning.

@vv  I apologize for the question again where did you find the asymptotic expansion of incomplete elliptic integrals in the case complex argument and modulus? I mean in what textbook? 

@vv  Thank you for the clarification. So the correct approximation of EllipticF(z,k) for large values of z is -EllipticCK(k)*I, right?

@Preben Alsholm a lot of thanks for your comment and your efforts. Frankly speaking I do not believe that a solution exists but I tried to find the interval of the parameter q where I can find roots. I worried that I do something wrong. That's why I decided to ask the community. 

@Preben Alsholm 

Thank you very much. It is the first time when I see the utilizing of the functiuon dsolve for the computation of the integral. Nice approach!

@Mariusz Iwaniuk 

Thank you for your help. I think the main problem is that Maple does not know the L'Hôpital's rule and how to solve the limit for the uncertainty 0*infinity :)


Wow! A lot of thanks! It looks amazing.

May I ask you additional question. My goal is to plot more complicated function (see the code below), which is represented by twice integration and subsequent summation. 


tt := -2; T_c := 0.169064e-1; mu := .869262; k := 2;
Omega := 2*Pi*N;
R0 := a*tanh((a^2-mu)/(2*T_c))*ln((2*a^2+2*a*q+q^2-2*mu-I*Omega)/(2*a^2-2*a*q+q^2-2*mu-I*Omega))/q-2;

R1 := int(R0, a = 0.1e-2 .. 100):

R2 := evalf(int(q*ln((-q^2-k^2+mu+I*(2*N*Pi-w)+k*q)/(-q^2-k^2+mu+I*(2*N*Pi-w)-k*q))/(k*(tt+evalf(R1))), q = 0.1e-2 .. 100));

R3 := evalf(Sum(R2, N = 0 .. 100)):

plot(Re(R3), w= 0.1e-2 .. 10);


As I understood my main problem is the integration procedure, namely the result of twice integration is not a number... Could you explain me, what was wrong?


Thanks for the help. I try to change infinities to the range n=-1000..1000 and it works. It gives me good approximation.

The problem is solved.


Sorry! I missed some part of the code. Here is the correct one

R0 := exp((2*Pi*I)*n^2*z);


R1 := sum(R0, n = -infinity .. infinity);

R1 := abs(R1)^2;
R2 := exp((2*Pi*I)*(n+1/2)^2*z);
R2 := evalf(sum(R2, n = -infinity .. infinity));
R2 := abs(R2)^2;
R := evalf(sqrt(Im(z))*(R1+R2));
plot(R, k = 1 .. 10);


A lot of thanks. I tested the code. It works great!.

I apologize but may I ask you again. I try to extend your code for three variables and plot the solutions. But at the end I get error

@Carl Love 

Thanks for your response. Nevertheless Maple can solve this system of Eqs. for given value of t. See below

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