> restart;
> dbeta:=beta*(sqrt(1-2*ln(epsilon)/beta^2)-1);

                            //    2 ln(epsilon)\1/2    \
              dbeta := beta ||1 - -------------|    - 1|
                            ||            2    |       |
                            \\        beta     /       /

> phi:=proc(x)
> 1/(2*Pi)^(N/2)*exp(-x*x/2)
> end:
> PHI:=proc(x)
> int(phi(t),t=-infinity..x)
> end:
> khi2:=proc(x,n)
> 1/GAMMA(n/2)*(1/2)^(n/2)*x^(n/2-1)*exp(-1/2*x)
> end:
> KHI2:=proc(x,n)
> int(khi2(t,n),t=0..x)
> end:
> 
> sol1:=solve(phi(beta+dbeta)/phi(beta)=epsilon,dbeta);
> sol2:=solve(PHI(-beta-dbeta)/PHI(-beta)=epsilon,dbeta);
> sol3:=solve((1-KHI2(beta+dbeta,6))/(1-KHI2(beta,6))=epsilon,dbeta);

                       2                 1/2
  sol1 := -beta + (beta  - 2 ln(epsilon))   ,

                     2                 1/2
        -beta - (beta  - 2 ln(epsilon))


               /
               | 1/2
  sol2 := -1/2 |2    beta
               \

                                                1/2                 \
                                               2    beta            |
         - 2 RootOf(-erf(_Z) + 1 + epsilon erf(---------) - epsilon)|
                                                   2                /

         1/2
        2


                               sol3 :=

> plot(subs(beta=5,n=2,[sol1[1],sol2,sol3]),epsilon=0.001..1);

> series(sol1[1]/sol2,epsilon);
Error, (in series/RootOf) unable to compute series

> with(stats);
Warning, these names have been redefined: anova, describe, fit,
importdata, random, statevalf, statplots, transform


  [anova, describe, fit, importdata, random, statevalf, statplots,

        transform]

> 
