> restart:
> with(Statistics):
> assume(u>0,alpha>0):
> chisquare_:=RandomVariable(ChiSquare(nu)):
> pdf:=subs(u=x,PDF(chisquare_,u));
> ddf:=factor(diff(pdf,x));
> cdf:=subs(u=x,CDF(chisquare_,u));
> cf:=CharacteristicFunction(chisquare_,x);
> mu_:=Mean(chisquare_);
> evalf[25](mu_);
> var_:=Variance(chisquare_);
> evalf[25](sqrt(var_));
> evalf[25](var_);
> skew_:=simplify((Skewness(chisquare_)));
> evalf[25](skew_);
> kurt_:=simplify((Kurtosis(chisquare_)));
> evalf[25](kurt_);
> #qdf:=Quantile(chisquare_,p);
> qdf:=proc(q,valnum)
>   fsolve(subs(valnum,cdf)=q,x)
> end:
> pdfgr:=[diff(pdf,nu)];
> cdfgr:=[diff(cdf,nu)];
> valnum:=nu=1.5;
> evalf(subs(valnum,x=1,ddf));
> evalf(subs(valnum,x=1,pdf));
> evalf(subs(valnum,x=1,cdf));
> evalf(subs(valnum,x=1,cf));
> evalf(subs(valnum,x=1,map(_x->_x,pdfgr)));
> evalf(subs(valnum,x=1,cdfgr));
> evalf(qdf(0.95,valnum));
> evalf(subs(valnum,mu_));
> evalf(subs(valnum,sqrt(var_)));
> evalf(subs(valnum,skew_));
> evalf(subs(valnum,kurt_));
> evalf(subs(valnum,var_));

                            / nu     \
                            |---- - 1|
                            \ 2      /
                           x           exp(- x/2)
                    pdf := ----------------------
                             / nu \
                             |----|
                             \ 2  /        nu
                            2       GAMMA(----)
                                           2


                       / nu     \
                       |---- - 1|
                       \ 2      /
                      x           exp(- x/2) (-2 + nu - x)
           ddf := 1/2 ------------------------------------
                              / nu \
                              |----|
                              \ 2  /        nu
                             2       GAMMA(----) x
                                            2


                                       nu
                                GAMMA(----, x/2)
                                       2
                     cdf := 1 - ----------------
                                         nu
                                  GAMMA(----)
                                         2


                                       /   nu \
                                       |- ----|
                                       \   2  /
                      cf := (1 - 2 I x)


                              mu_ := nu


                                  nu


                             var_ := 2 nu


                                                1/2
                   1.414213562373095048801689 nu


                                2. nu


                                       1/2
                                    2 2
                           skew_ := ------
                                      1/2
                                    nu


                      2.828427124746190097603378
                      --------------------------
                                  1/2
                                nu


                                  3 (4 + nu)
                         kurt_ := ----------
                                      nu


                             3. (4. + nu)
                             ------------
                                  nu


                  / nu     \
                  |---- - 1|
                  \ 2      /
                 x           exp(- x/2) ln(2)
  pdfgr := [-1/2 ----------------------------
                      / nu \
                      |----|
                      \ 2  /        nu
                     2       GAMMA(----)
                                    2

                / nu     \
                |---- - 1|
                \ 2      /                 nu
               x           exp(- x/2) Psi(----)
                                           2
         - 1/2 --------------------------------
                      / nu \
                      |----|
                      \ 2  /        nu
                     2       GAMMA(----)
                                    2

                / nu     \
                |---- - 1|
                \ 2      /
               x           ln(x) exp(- x/2)
         + 1/2 ----------------------------]
                    / nu \
                    |----|
                    \ 2  /        nu
                   2       GAMMA(----)
                                  2


              /           nu
  cdfgr := [- |1/2 GAMMA(----, x/2) ln(x/2)
              \           2

                                              nu             \   /
         + 1/2 MeijerG([[], [1, 1]], [[0, 0, ----], []], x/2)|  /
                                              2              / /

                                 nu             nu
                          GAMMA(----, x/2) Psi(----)
               nu                2              2
        GAMMA(----) + 1/2 --------------------------]
               2                        nu
                                 GAMMA(----)
                                        2


                          valnum := nu = 1.5


                            -0.2207281535


                             0.2943042047


                             0.5279371097


                    0.3689252084 + 0.4036879325 I


                            [0.0577886465]


                           [-0.2917142294]


                             4.980195284


                                 1.5


                             1.732050807


                             2.309401076


                             11.00000000


                                 3.0

> combine(factor(pdfgr[1]/pdf),ln);

                                         1/2  1/2
                              nu        2    x
                    -1/2 Psi(----) + ln(---------)
                              2             2

> 
