% I101 The integral I_{1,[01]}(a,b). 
%      Input:
%      N  ... the maximum number of recurrence coefficients
%             needed
%      n0 ... an estimate of the number of recurrence
%             coefficients needed
%
function y=I101(N,n0,a,b)
eps0=.5e-12; eta=1/100;
k0=k_0(eps0,a,b); 
ab=r_jacobi01(N);
err=1; s1=0;
n=n0;
while err>eps0
  s0=s1; n=n+2;
  if n>N
    error('n exceeds N in I101.m')
    break
  end
  xw=gauss(n,ab);
  s1=0;
  for k=1:n
    t=eta+(1-eta)*xw(k,1);
    y=-t*exp(-t);
    w=wofy1(y);
    w=(-w)^a*t^(-b);
    s1=s1+xw(k,2)*w; 
  end
  s1=(1-eta)*s1;
  err=abs((s1-s0)/s1);
end
int=0;
for k=2:k0+1
  if k<=k0
    c=10^(-(k+1)); d=10^(-k);
  else
    c=0; d=10^(-k);
  end
  err=1; int1=0; 
  n=0; nmax=0;
  while err>eps0
    n=n+2;
    int0=int1;
    xw=gauss(n,ab);
    s=0;
    for nu=1:n
      x=c+xw(nu,1)*(d-c);
      w=wofy1(-x*exp(-x));
      w=(-w)^a*x^(-b);
      s=s+xw(nu,2)*w;
    end
    int1=(d-c)*s;
    err=abs(int1-int0);
  end
  if n>nmax
    nmax=n;
  end
  int=int+int1;
end
y=s1+int;