problem with solving integral

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Mahboubeh Shahrbaf
Mahboubeh Shahrbaf 2020-12-21
评论： Mahboubeh Shahrbaf 2020-12-22
Dear all,
I am trying to solve a symbolic integral via matlab.
But I just got the modifed form of my integral as the answer.
What is the problem?
The integral is getting from a popular paper and should not be any problem in it.
I want to reproduce the results of the paper.
T=10.;
mu=0.;
mustar = 400.;
Lambda = 602.3;
GsLambda2 = 2.319;
Gs = 0.00000639;
m0 = 5.5;
m = 100.;
Gv = 0.5 * Gs;
Gd = 0.75 * Gs;
syms p d
int(p.^2.*(((1.-2.*((exp (( sqrt (( sqrt (p.^2.+m.^2.) - mustar ).^2 + ...
d.^2))/T) +1).^(-1)))/(sqrt (( sqrt (p.^2.+m.^2.) - mustar).^2 + d.^2))) + ...
((1. - 2.*((exp (( sqrt (( sqrt (p.^2 + m.^2) + mustar).^2 + d.^2))/T)...
+ 1).^(-1)))/(sqrt (( sqrt (p.^2+m.^2) + mustar).^2 + d.^2)))), p, 0, 602.3)
ans =
int(-p^2*((2/(exp((((p^2 + 10000)^(1/2) - 400)^2 + d^2)^(1/2)/10) + 1) - 1)/(((p^2 + 10000)^(1/2) - 400)^2 + d^2)^(1/2) + (2/(exp((((p^2 + 10000)^(1/2) + 400)^2 + d^2)^(1/2)/10) + 1) - 1)/(((p^2 + 10000)^(1/2) + 400)^2 + d^2)^(1/2)), p, 0, 6023/10)
I would really appreciate it if some one could help me.

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回答（1 个）

Star Strider
Star Strider 2020-12-21
I suspect that the paper did not have an analytical expression for the integral, or you would be evaluating it.
Integrate it numerically instead:
T=10.;
mu=0.;
mustar = 400.;
Lambda = 602.3;
GsLambda2 = 2.319;
Gs = 0.00000639;
m0 = 5.5;
m = 100.;
Gv = 0.5 * Gs;
Gd = 0.75 * Gs;
% syms p d
dfcn = @(d) integral(@(p) p.^2.*(((1.-2.*((exp (( sqrt (( sqrt (p.^2.+m.^2.) - mustar ).^2 + ...
d.^2))/T) +1).^(-1)))./(sqrt (( sqrt (p.^2.+m.^2.) - mustar).^2 + d.^2))) + ...
((1. - 2.*((exp (( sqrt (( sqrt (p.^2 + m.^2) + mustar).^2 + d.^2))/T)...
+ 1).^(-1)))./(sqrt (( sqrt (p.^2+m.^2) + mustar).^2 + d.^2)))), 0, 602.3, 'ArrayValued',1);
d = 0:1000; % Create Values For ‘d’
Result = dfcn(d);
figure
plot(d, Result)
grid
.
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Walter Roberson
Walter Roberson 2020-12-22
I would have to look more closely... but the new equations you posted do not look to me to be the same as the code.
With the code that was posted, I think there is no realistic hope of coming up with a symbolic integral in d.
Mahboubeh Shahrbaf
Mahboubeh Shahrbaf 2020-12-22
Actually, the integral in the code is exactly the same as one which is in the equation I've posted.
Just I ignored the constant coefficients.
OK, thank you both Star Strider and Walter Roberson.
Then, I have to find another routine to solve directly the integral equations.

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