> restart:
> Rfs:=(int((diff(1/sqrt(2*Pi)*exp(-x*x/2),x$2))^2,x=-infinity..infinity
> ));
> assume(x>0,x<1):
> _beta:=Beta(a,b);
> _betaInc:=int(t^(a-1)*(1-t)^(b-1),t=0..x);
> _betaRatioInc:=_betaInc/beta;
> valnum:=a=3.5,b=5.6:
> valx:=x=0.3:
> valy:=y=0.002:
> beta:=evalf(subs(valnum,_beta));
> betaInc:=evalf(subs(valnum,valx,_betaInc));
> betaRatioInc:=evalf(subs(valnum,valx,_betaRatioInc));
> betaIncInv:=fsolve(subs(valnum,_betaInc)=subs(valy,y),x,0..1);
> betaRatioIncInv:=fsolve(subs(valnum,_betaRatioInc)=subs(valy,y),x,0..1
> );

                         _beta := Beta(a, b)


                       a
                     x~  hypergeom([a, -b + 1], [1 + a], x~)
         _betaInc := ---------------------------------------
                                        a


                          a
                        x~  hypergeom([a, -b + 1], [1 + a], x~)
       _betaRatioInc := ---------------------------------------
                                        a beta


                        beta := 0.004093457689


                      betaInc := 0.001297399181


                     betaRatioInc := 0.3169445686


                      betaIncInv := 0.3711124504


                   betaRatioIncInv := 0.05322108266

> 
