How to avoid multiple integration of the function and speed up calculations?

Hello. I'm dealing with with the code, where I have to integrate complicated function S(q,k) over q. Then I have to make summation over the integer m from zero to m=100 and finally I have to perform integration over k. Until the final integration over k the code's execution takes about 4 minutes on my laptop. The main problem is very long integration procedure over k, about 6 hours! I understand the slow work is caused by the length of the vector R, which has 1001 elements and this produces 1001 times of integration of the function R(k). But I can't modify my code in a proper way in order to avoid this multiple integration and significantly speed up calculation. I will kindly appreciate for any help.

function z=test
tic

tt=-0.000689609;

t=0.242731;
muu=0.365908;

[m,NN]=meshgrid(0:100,-500:1:500);

      fun1=@(a,q,N) a.*tanh((a.^2-muu)./(2*t)).*log((2*a.^2+2*a.*q+q.^2-2*muu-1i*2*pi*N*t)./(2*a.^2-2*a.*q+q.^2-2*muu-1i*2*pi*N*t))./q-2;
      Gamma_0=@(q,N) tt*pi+integral(@(a)fun1(a,q,N),0,10000,'AbsTol',1e-6,'RelTol',1e-3,'ArrayValued',true);

      y1= @(N,q,k) t*q./k*log((-k.^2+2*k.*q-q.^2+muu+1i*(2*pi*N.*t-(2*m+1)*pi*t))./(-k.^2-2*k.*q-q.^2+muu+1i*(2*pi*N.*t-(2*m+1)*pi*t)))./Gamma_0(q,N);
      R1=@(q,k) integral(@(N)y1(N,q,k),500,1000000,'AbsTol',1e-6,'RelTol',1e-3,'ArrayValued',true)+1.88*t*(1/2000)*sqrt(2)/(pi^(3/2)*(1i*t)^(3/2))*q.^2;%1.896
      R11=@(q,k) integral(@(N)y1(N,q,k),-1000000,-500,'AbsTol',1e-6,'RelTol',1e-3,'ArrayValued',true)+conj(1.88*t*(1/2000)*sqrt(2)/(pi^(3/2)*(1i*t)^(3/2))*q.^2);
      y2=@(q,k) t*q./k*log((-k.^2+2*k.*q-q.^2+muu+1i*(2*pi*NN(:,1).*t-(2*m(1,:)+1)*pi*t))./(-k.^2-2*k.*q-q.^2+muu+1i*(2*pi*NN(:,1).*t-(2*m(1,:)+1)*pi*t)))./Gamma_0(q,NN(:,1));
      R2=@(q,k) sum(y2(q,k));
      S=@(q,k) R1(q,k)+R11(q,k)+R2(q,k);

      Sigma=@(k) integral(@(q)S(q,k),0.001,10,'AbsTol',1e-6,'RelTol',1e-3,'ArrayValued',true);

      R=@(k) 2*sum(exp(1i*(2*m(1,:)+1)*pi*t*10^(-11))./(1i*(2*m(1,:)+1)*pi*t-Sigma(k)),2);

      Number=integral(@(k) R(k),0.001,5,'AbsTol',1e-6,'RelTol',1e-3,'ArrayValued',true);
      Number(1,:)
  toc
  end