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legendre_q-sqrt

legendre_q(8,-i/sqrt(...

Calculate

legendre_q

? legendre_q;

Calculate

legendre_q

legendre_q(3,x);

Calculate

legendre_q

legendre_q(8,0.5);

Calculate

legendre_q-sqrt

legendre_q(3,sqrt(3));

Calculate

legendre_q-sqrt

legendre_q(8,-i/sqrt(...

Calculate

legendre_q

? legendre_q;

Calculate

legendre_q

legendre_q(3,x);

Calculate

legendre_q

legendre_q(8,0.5);

Calculate

legendre_q-sqrt

legendre_q(3,sqrt(3));

Calculate

legendre_q

Run Example
(%i1)a:-%i/(3^(0.5));
(%o1)                        - 0.57735026918963 %i
(%i2) a:%ig(x):= ((x^2-1)^(-1/2))*assoc_legendre_q(8,-1,x);
                                 - 1
                                 ---
                           2      2
(%o2)          %ig(x) := (x  - 1)    assoc_legendre_q(8, - 1, x)
(%i3) g(x):= legendre_q(5,x);
(%o3)                      g(x) := legendre_q(5, x)
(%i4) expand(g(a));
                             - 1
                             ---
                       2      2     - 1    5
(%o4) (63 (%ig(x) := (x  - 1)    "Q"   (x))
                                    8
                            - 1
                            ---
                      2      2     - 1
          %ig(x) := (x  - 1)    "Q"   (x)
                                   8
 log(- -------------------------------------
                          - 1
                          ---
                    2      2     - 1
       (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                 8
                     1
 - -------------------------------------))/16
                      - 1
                      ---
                2      2     - 1
   (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                             8
                          - 1
                          ---
                    2      2     - 1    3
 - (35 (%ig(x) := (x  - 1)    "Q"   (x))
                                 8
                            - 1
                            ---
                      2      2     - 1
          %ig(x) := (x  - 1)    "Q"   (x)
                                   8
 log(- -------------------------------------
                          - 1
                          ---
                    2      2     - 1
       (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                 8
                     1
 - -------------------------------------))/8
                      - 1
                      ---
                2      2     - 1
   (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                             8
                          - 1
                          ---
                    2      2     - 1
 + (15 (%ig(x) := (x  - 1)    "Q"   (x))
                                 8
                            - 1
                            ---
                      2      2     - 1
          %ig(x) := (x  - 1)    "Q"   (x)
                                   8
 log(- -------------------------------------
                          - 1
                          ---
                    2      2     - 1
       (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                 8
                     1
 - -------------------------------------))/16
                      - 1
                      ---
                2      2     - 1
   (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                             8
                         - 1
                         ---
                   2      2     - 1    4
   63 (%ig(x) := (x  - 1)    "Q"   (x))
                                8
 - -------------------------------------
                     8
                         - 1
                         ---
                   2      2     - 1    2
   49 (%ig(x) := (x  - 1)    "Q"   (x))
                                8          8
 + ------------------------------------- - --
                     8                     15
(%i5) g1(x):=''(diff(g(x),x));
                             x + 1   6        5             x + 1   4        3
(%o5)/R/ g1(x) := (315 log(- -----) x  - 630 x  - 525 log(- -----) x  + 840 x
                             x - 1                          x - 1
                              x + 1   2                    x + 1        2
                  + 225 log(- -----) x  - 226 x - 15 log(- -----))/(16 x  - 16)
                              x - 1                        x - 1
(%i6) expand(g1(a));
                              - 1
                              ---
                        2      2     - 1    6
(%o6) (315 (%ig(x) := (x  - 1)    "Q"   (x))
                                     8
                            - 1
                            ---
                      2      2     - 1
          %ig(x) := (x  - 1)    "Q"   (x)
                                   8
 log(- -------------------------------------
                          - 1
                          ---
                    2      2     - 1
       (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                 8
                     1
 - -------------------------------------))
                      - 1
                      ---
                2      2     - 1
   (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                             8
                        - 1
                        ---
                  2      2     - 1    2
/(16 (%ig(x) := (x  - 1)    "Q"   (x))  - 16)
                               8
                           - 1
                           ---
                     2      2     - 1    4
 - (525 (%ig(x) := (x  - 1)    "Q"   (x))
                                  8
                            - 1
                            ---
                      2      2     - 1
          %ig(x) := (x  - 1)    "Q"   (x)
                                   8
 log(- -------------------------------------
                          - 1
                          ---
                    2      2     - 1
       (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                 8
                     1
 - -------------------------------------))
                      - 1
                      ---
                2      2     - 1
   (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                             8
                        - 1
                        ---
                  2      2     - 1    2
/(16 (%ig(x) := (x  - 1)    "Q"   (x))  - 16)
                               8
                           - 1
                           ---
                     2      2     - 1    2
 + (225 (%ig(x) := (x  - 1)    "Q"   (x))
                                  8
                            - 1
                            ---
                      2      2     - 1
          %ig(x) := (x  - 1)    "Q"   (x)
                                   8
 log(- -------------------------------------
                          - 1
                          ---
                    2      2     - 1
       (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                 8
                     1
 - -------------------------------------))
                      - 1
                      ---
                2      2     - 1
   (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                             8
                        - 1
                        ---
                  2      2     - 1    2
/(16 (%ig(x) := (x  - 1)    "Q"   (x))  - 16)
                               8
                                  - 1
                                  ---
                            2      2     - 1
                %ig(x) := (x  - 1)    "Q"   (x)
                                         8
 - (15 log(- -------------------------------------
                                - 1
                                ---
                          2      2     - 1
             (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                       8
                     1
 - -------------------------------------))
                      - 1
                      ---
                2      2     - 1
   (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                             8
                        - 1
                        ---
                  2      2     - 1    2
/(16 (%ig(x) := (x  - 1)    "Q"   (x))  - 16)
                               8
                            - 1
                            ---
                      2      2     - 1    5
     630 (%ig(x) := (x  - 1)    "Q"   (x))
                                   8
 - ------------------------------------------
                         - 1
                         ---
                   2      2     - 1    2
   16 (%ig(x) := (x  - 1)    "Q"   (x))  - 16
                                8
                            - 1
                            ---
                      2      2     - 1    3
     840 (%ig(x) := (x  - 1)    "Q"   (x))
                                   8
 + ------------------------------------------
                         - 1
                         ---
                   2      2     - 1    2
   16 (%ig(x) := (x  - 1)    "Q"   (x))  - 16
                                8
                            - 1
                            ---
                      2      2     - 1
      226 %ig(x) := (x  - 1)    "Q"   (x)
                                   8
 - ------------------------------------------
                         - 1
                         ---
                   2      2     - 1    2
   16 (%ig(x) := (x  - 1)    "Q"   (x))  - 16
                                8
(%i7) A1:(4.0)/(7.0);
(%o7)                          0.57142857142857
(%i8) B:(125*25)/(56*21);
                                     3125
(%o8)                                ----
                                     1176
(%i9) E:(125)/(1512);
                                     125
(%o9)                                ----
                                     1512
(%i10) F:(-25)/(196);
                                       25
(%o10)                               - ---
                                       196
(%i11) Exp1:B+a*A1*E*2.0*a/((1-a*a)^2)-F-E/(1-a*a);
                              125
(%o11) - ---------------------------------------------
                                      - 1
                                      ---
                                2      2     - 1    2
         1512 (1 - (%ig(x) := (x  - 1)    "Q"   (x)) )
                                             8
                                                         - 1
                                                         ---
                                                   2      2     - 1    2
                     0.09448223733938 (%ig(x) := (x  - 1)    "Q"   (x))
                                                                8          3275
                   + --------------------------------------------------- + ----
                                                  - 1                      1176
                                                  ---
                                            2      2     - 1    2 2
                          (1 - (%ig(x) := (x  - 1)    "Q"   (x)) )
                                                         8
(%i12) Exp1:9/200+27*3/50;
                                      333
(%o12)                                ---
                                      200
(%i13) Exp2: g(a)-a*A1*g1(a);

rat: replaced 0.57142857142857 by 4/7 = 0.57142857142857
                                            - 1
                                            ---
                                      2      2     - 1
                         (%ig(x) := (x  - 1)    "Q"   (x)) + 1
                                                   8
(%o13)/R/ - (12285 log(- -------------------------------------)
                                            - 1
                                            ---
                                      2      2     - 1
                         (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                                   8
                    - 1                                        - 1
                    ---                                        ---
              2      2     - 1    7                      2      2     - 1    6
 (%ig(x) := (x  - 1)    "Q"   (x))  - 24570 (%ig(x) := (x  - 1)    "Q"   (x))
                           8                                          8
                                  - 1
                                  ---
                            2      2     - 1
               (%ig(x) := (x  - 1)    "Q"   (x)) + 1
                                         8
 - 17535 log(- -------------------------------------)
                                  - 1
                                  ---
                            2      2     - 1
               (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                         8
                    - 1                                        - 1
                    ---                                        ---
              2      2     - 1    5                      2      2     - 1    4
 (%ig(x) := (x  - 1)    "Q"   (x))  + 26880 (%ig(x) := (x  - 1)    "Q"   (x))
                           8                                          8
                                 - 1
                                 ---
                           2      2     - 1
              (%ig(x) := (x  - 1)    "Q"   (x)) + 1
                                        8
 + 4575 log(- -------------------------------------)
                                 - 1
                                 ---
                           2      2     - 1
              (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                        8
                    - 1                                       - 1
                    ---                                       ---
              2      2     - 1    3                     2      2     - 1    2
 (%ig(x) := (x  - 1)    "Q"   (x))  - 2374 (%ig(x) := (x  - 1)    "Q"   (x))
                           8                                         8
                                - 1
                                ---
                          2      2     - 1
             (%ig(x) := (x  - 1)    "Q"   (x)) + 1
                                       8
 + 675 log(- -------------------------------------)
                                - 1
                                ---
                          2      2     - 1
             (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                       8
                    - 1
                    ---
              2      2     - 1
 (%ig(x) := (x  - 1)    "Q"   (x)) - 896)
                           8
                          - 1
                          ---
                    2      2     - 1    2
/(1680 (%ig(x) := (x  - 1)    "Q"   (x))  - 1680)
                                 8
(%i14) Exp2: g(a)+ a*(12/30)*g1(a);
                                         - 1
                                         ---
                                   2      2     - 1
                      (%ig(x) := (x  - 1)    "Q"   (x)) + 1
                                                8
(%o14)/R/ (2835 log(- -------------------------------------)
                                         - 1
                                         ---
                                   2      2     - 1
                      (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                                8
                    - 1                                       - 1
                    ---                                       ---
              2      2     - 1    7                     2      2     - 1    6
 (%ig(x) := (x  - 1)    "Q"   (x))  - 5670 (%ig(x) := (x  - 1)    "Q"   (x))
                           8                                         8
                                 - 1
                                 ---
                           2      2     - 1
              (%ig(x) := (x  - 1)    "Q"   (x)) + 1
                                        8
 - 5145 log(- -------------------------------------)
                                 - 1
                                 ---
                           2      2     - 1
              (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                        8
                    - 1                                       - 1
                    ---                                       ---
              2      2     - 1    5                     2      2     - 1    4
 (%ig(x) := (x  - 1)    "Q"   (x))  + 8400 (%ig(x) := (x  - 1)    "Q"   (x))
                           8                                         8
                                 - 1
                                 ---
                           2      2     - 1
              (%ig(x) := (x  - 1)    "Q"   (x)) + 1
                                        8
 + 2625 log(- -------------------------------------)
                                 - 1
                                 ---
                           2      2     - 1
              (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                        8
                    - 1                                       - 1
                    ---                                       ---
              2      2     - 1    3                     2      2     - 1    2
 (%ig(x) := (x  - 1)    "Q"   (x))  - 2954 (%ig(x) := (x  - 1)    "Q"   (x))
                           8                                         8
                                - 1
                                ---
                          2      2     - 1
             (%ig(x) := (x  - 1)    "Q"   (x)) + 1
                                       8
 - 315 log(- -------------------------------------)
                                - 1
                                ---
                          2      2     - 1
             (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                       8
                    - 1
                    ---
              2      2     - 1
 (%ig(x) := (x  - 1)    "Q"   (x)) + 128)
                           8
                         - 1
                         ---
                   2      2     - 1    2
/(240 (%ig(x) := (x  - 1)    "Q"   (x))  - 240)
                                8
(%i15) C2:expand(Exp1/Exp2);
                                - 1
                                ---
                          2      2     - 1    2
(%o15) (1998 (%ig(x) := (x  - 1)    "Q"   (x)) )
                                       8
                           - 1
                           ---
                     2      2     - 1    7
/(14175 (%ig(x) := (x  - 1)    "Q"   (x))
                                  8
                            - 1
                            ---
                      2      2     - 1
          %ig(x) := (x  - 1)    "Q"   (x)
                                   8
 log(- -------------------------------------
                          - 1
                          ---
                    2      2     - 1
       (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                 8
                     1
 - -------------------------------------)
                      - 1
                      ---
                2      2     - 1
   (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                             8
                            - 1
                            ---
                      2      2     - 1    5
 - 25725 (%ig(x) := (x  - 1)    "Q"   (x))
                                   8
                            - 1
                            ---
                      2      2     - 1
          %ig(x) := (x  - 1)    "Q"   (x)
                                   8
 log(- -------------------------------------
                          - 1
                          ---
                    2      2     - 1
       (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                 8
                     1
 - -------------------------------------)
                      - 1
                      ---
                2      2     - 1
   (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                             8
                            - 1
                            ---
                      2      2     - 1    3
 + 13125 (%ig(x) := (x  - 1)    "Q"   (x))
                                   8
                            - 1
                            ---
                      2      2     - 1
          %ig(x) := (x  - 1)    "Q"   (x)
                                   8
 log(- -------------------------------------
                          - 1
                          ---
                    2      2     - 1
       (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                 8
                     1
 - -------------------------------------)
                      - 1
                      ---
                2      2     - 1
   (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                             8
                           - 1
                           ---
                     2      2     - 1
 - 1575 (%ig(x) := (x  - 1)    "Q"   (x))
                                  8
                            - 1
                            ---
                      2      2     - 1
          %ig(x) := (x  - 1)    "Q"   (x)
                                   8
 log(- -------------------------------------
                          - 1
                          ---
                    2      2     - 1
       (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                 8
                     1
 - -------------------------------------)
                      - 1
                      ---
                2      2     - 1
   (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                             8
                            - 1
                            ---
                      2      2     - 1    6
 - 28350 (%ig(x) := (x  - 1)    "Q"   (x))
                                   8
                            - 1
                            ---
                      2      2     - 1    4
 + 42000 (%ig(x) := (x  - 1)    "Q"   (x))
                                   8
                            - 1
                            ---
                      2      2     - 1    2
 - 14770 (%ig(x) := (x  - 1)    "Q"   (x))  + 640)
                                   8
                                  - 1
                                  ---
                            2      2     - 1    7
 - 1998/(14175 (%ig(x) := (x  - 1)    "Q"   (x))
                                         8
                            - 1
                            ---
                      2      2     - 1
          %ig(x) := (x  - 1)    "Q"   (x)
                                   8
 log(- -------------------------------------
                          - 1
                          ---
                    2      2     - 1
       (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                 8
                     1
 - -------------------------------------)
                      - 1
                      ---
                2      2     - 1
   (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                             8
                            - 1
                            ---
                      2      2     - 1    5
 - 25725 (%ig(x) := (x  - 1)    "Q"   (x))
                                   8
                            - 1
                            ---
                      2      2     - 1
          %ig(x) := (x  - 1)    "Q"   (x)
                                   8
 log(- -------------------------------------
                          - 1
                          ---
                    2      2     - 1
       (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                 8
                     1
 - -------------------------------------)
                      - 1
                      ---
                2      2     - 1
   (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                             8
                            - 1
                            ---
                      2      2     - 1    3
 + 13125 (%ig(x) := (x  - 1)    "Q"   (x))
                                   8
                            - 1
                            ---
                      2      2     - 1
          %ig(x) := (x  - 1)    "Q"   (x)
                                   8
 log(- -------------------------------------
                          - 1
                          ---
                    2      2     - 1
       (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                 8
                     1
 - -------------------------------------)
                      - 1
                      ---
                2      2     - 1
   (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                             8
                           - 1
                           ---
                     2      2     - 1
 - 1575 (%ig(x) := (x  - 1)    "Q"   (x))
                                  8
                            - 1
                            ---
                      2      2     - 1
          %ig(x) := (x  - 1)    "Q"   (x)
                                   8
 log(- -------------------------------------
                          - 1
                          ---
                    2      2     - 1
       (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                                 8
                     1
 - -------------------------------------)
                      - 1
                      ---
                2      2     - 1
   (%ig(x) := (x  - 1)    "Q"   (x)) - 1
                             8
                            - 1
                            ---
                      2      2     - 1    6
 - 28350 (%ig(x) := (x  - 1)    "Q"   (x))
                                   8
                            - 1
                            ---
                      2      2     - 1    4
 + 42000 (%ig(x) := (x  - 1)    "Q"   (x))
                                   8
                            - 1
                            ---
                      2      2     - 1    2
 - 14770 (%ig(x) := (x  - 1)    "Q"   (x))  + 640)
                                   8
(%i16) 
Run Example
y:%i*1;
(%o1)                                 %i
(%i2) f(x):= legendre_q(5,x);
(%o2)                      f(x) := legendre_q(5, x)
(%i3) f1(x):=''(diff(f(x),x));
                             x + 1   6        5             x + 1   4        3
(%o3)/R/ f1(x) := (315 log(- -----) x  - 630 x  - 525 log(- -----) x  + 840 x
                             x - 1                          x - 1
                              x + 1   2                    x + 1        2
                  + 225 log(- -----) x  - 226 x - 15 log(- -----))/(16 x  - 16)
                              x - 1                        x - 1
(%i4) f(y);
                    %i + 1    5          4              %i + 1    3          2
(%o4)/R/ (945 log(- ------) %i  - 1890 %i  - 1050 log(- ------) %i  + 1470 %i
                    %i - 1                              %i - 1
                                                          %i + 1
                                              + 225 log(- ------) %i - 128)/240
                                                          %i - 1
(%i5) f1(y);
                                    %i + 1
                          135 log(- ------) + 212 %i
                                    %i - 1
(%o5)/R/                  --------------------------
                                      4
(%i6) a1:expand(realpart(f(y)));
                                  37 %pi   218
(%o6)                           - ------ - ---
                                    8      15
(%i7) expand(imagpart(f(y)));
(%o7)                                  0
(%i8) expand(realpart(f1(y)));
(%o8)                                  0
(%i9) b1:expand(imagpart(f1(y)));
                                 135 %pi
(%o9)                            ------- + 53
                                    8
(%i10) c:(333/200)*(a1+6*b1/15);
                             135 %pi
                          2 (------- + 53)
                                8            37 %pi   218
                     333 (---------------- - ------ - ---)
                                 5             8      15
(%o10)               -------------------------------------
                                      200
(%i11) expand(c);
                                5661 %pi   111
(%o11)                          -------- + ---
                                  1600     10
(%i12) 
Run Example
f(x):= x+1;
(%o1)                            f(x) := x + 1
(%i2) g(1);
(%o2)                                g(1)
(%i3) g(x):= ((x^2-1)^(-1/2))*assoc_legendre_q(8,-1,x);
                                - 1
                                ---
                          2      2
(%o3)           g(x) := (x  - 1)    assoc_legendre_q(8, - 1, x)
(%i4) expand(g(x1));
                 9            2          x1       1
        225225 x1  sqrt(1 - x1 ) log(- ------ - ------)
                                       x1 - 1   x1 - 1
(%o4) - -----------------------------------------------
                 2        2                     2
         80640 x1  sqrt(x1  - 1) - 80640 sqrt(x1  - 1)
            7            2          x1       1
   540540 x1  sqrt(1 - x1 ) log(- ------ - ------)
                                  x1 - 1   x1 - 1
 + -----------------------------------------------
            2        2                     2
    80640 x1  sqrt(x1  - 1) - 80640 sqrt(x1  - 1)
            5            2          x1       1
   436590 x1  sqrt(1 - x1 ) log(- ------ - ------)
                                  x1 - 1   x1 - 1
 - -----------------------------------------------
            2        2                     2
    80640 x1  sqrt(x1  - 1) - 80640 sqrt(x1  - 1)
            3            2          x1       1
   132300 x1  sqrt(1 - x1 ) log(- ------ - ------)
                                  x1 - 1   x1 - 1
 + -----------------------------------------------
            2        2                     2
    80640 x1  sqrt(x1  - 1) - 80640 sqrt(x1  - 1)
                       2          x1       1
   11025 x1 sqrt(1 - x1 ) log(- ------ - ------)
                                x1 - 1   x1 - 1
 - ---------------------------------------------
           2        2                     2
   80640 x1  sqrt(x1  - 1) - 80640 sqrt(x1  - 1)
                      8            2
             450450 x1  sqrt(1 - x1 )
 + ---------------------------------------------
           2        2                     2
   80640 x1  sqrt(x1  - 1) - 80640 sqrt(x1  - 1)
                      6            2
             930930 x1  sqrt(1 - x1 )
 - ---------------------------------------------
           2        2                     2
   80640 x1  sqrt(x1  - 1) - 80640 sqrt(x1  - 1)
                      4            2
             602910 x1  sqrt(1 - x1 )
 + ---------------------------------------------
           2        2                     2
   80640 x1  sqrt(x1  - 1) - 80640 sqrt(x1  - 1)
                      2            2
             125406 x1  sqrt(1 - x1 )
 - ---------------------------------------------
           2        2                     2
   80640 x1  sqrt(x1  - 1) - 80640 sqrt(x1  - 1)
                                2
                4096 sqrt(1 - x1 )
 + ---------------------------------------------
           2        2                     2
   80640 x1  sqrt(x1  - 1) - 80640 sqrt(x1  - 1)
(%i5) g1(x):=''(diff(g(x),x));
                                 x + 1            2 2
(%o5)/R/ g1(x) := ((225225 log(- -----) sqrt(1 - x )
                                 x - 1
                2     2       x + 1    12
 + 225225 sqrt(x  - 1)  log(- -----)) x
                              x - 1
                       2 2                2     2   11
 + (- 450450 sqrt(1 - x )  - 450450 sqrt(x  - 1) ) x
                     2     2                 x + 1            2 2
 + ((- 1576575 sqrt(x  - 1)  - 765765) log(- -----) sqrt(1 - x )
                                             x - 1
                2     2       x + 1    10
 - 765765 sqrt(x  - 1)  log(- -----)) x
                              x - 1
                   2     2                      2 2                 2     2   9
 + ((3153150 sqrt(x  - 1)  + 1381380) sqrt(1 - x )  + 1381380 sqrt(x  - 1) ) x
                   2     2                 x + 1            2 2
 + ((4729725 sqrt(x  - 1)  + 977130) log(- -----) sqrt(1 - x )
                                           x - 1
                2     2       x + 1    8
 + 977130 sqrt(x  - 1)  log(- -----)) x
                              x - 1
                     2     2                      2 2                 2     2
 + ((- 8408400 sqrt(x  - 1)  - 1533840) sqrt(1 - x )  - 1533840 sqrt(x  - 1) )
  7                     2     2                 x + 1            2 2
 x  + ((- 5093550 sqrt(x  - 1)  - 568890) log(- -----) sqrt(1 - x )
                                                x - 1
                2     2       x + 1    6
 - 568890 sqrt(x  - 1)  log(- -----)) x
                              x - 1
                   2     2                     2 2                2     2   5
 + ((7664580 sqrt(x  - 1)  + 728316) sqrt(1 - x )  + 728316 sqrt(x  - 1) ) x
                   2     2                 x + 1            2 2
 + ((2315250 sqrt(x  - 1)  + 143325) log(- -----) sqrt(1 - x )
                                           x - 1
                2     2       x + 1    4
 + 143325 sqrt(x  - 1)  log(- -----)) x
                              x - 1
                     2     2                     2 2                2     2   3
 + ((- 2676240 sqrt(x  - 1)  - 129502) sqrt(1 - x )  - 129502 sqrt(x  - 1) ) x
                    2     2                x + 1            2 2
 + ((- 385875 sqrt(x  - 1)  - 11025) log(- -----) sqrt(1 - x )
                                           x - 1
               2     2       x + 1    2
 - 11025 sqrt(x  - 1)  log(- -----)) x
                             x - 1
                  2     2                   2 2              2     2
 + ((264670 sqrt(x  - 1)  + 4096) sqrt(1 - x )  + 4096 sqrt(x  - 1) ) x
               2     2       x + 1            2 2
 + 11025 sqrt(x  - 1)  log(- -----) sqrt(1 - x ) )
                             x - 1
              2     3           2   4                2     3           2   2
/(80640 sqrt(x  - 1)  sqrt(1 - x ) x  - 161280 sqrt(x  - 1)  sqrt(1 - x ) x
               2     3           2
 + 80640 sqrt(x  - 1)  sqrt(1 - x ))
(%i6) expand(g1(-%i));
                                   %i         1
                     175 %i log(-------- - --------)
                                - %i - 1   - %i - 1    1237
(%o6)              - ------------------------------- - ----
                                    4                   18
(%i7) 

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