function(x,k=10){
# this function computes the upper tail probability K(x)
# for the limit distribution of D*sqrt((m+n)/(m*n)) 
# to an absolute error of epsilon 1e-7
epsilon = 1e-7
j = seq(1,k,1)
y = 2*sum(((-1)^(j+1))*exp(-2*j^2*x^2))
k2=2*k
j = seq(1,k2,1)
y2 = 2*sum(((-1)^(j+1))*exp(-2*j^2*x^2))
if(y2==0) return(0)
while(abs(y2-y)> epsilon){
k=k2
y=y2
k2=2*k
j = seq(1,k2,1)
y2=2*sum((-1)^(j+1)*exp(-2*j^2*x^2))
}
list(y2,k2)
}