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gamma-linsolve-solve

eq1:x*4+y-2=y;

eq2:x+2=y;

eq3: pi*(1+(x-((a-1)/...

Calculate

gamma

gamma(7+8*i);

Calculate

gamma-inf-sum

sum(((gamma(k+3))*(su...

evaluate;

Calculate

gamma-inf-limit

limit ((gamma(x + 72 ...

Calculate

gamma-linsolve

eq1:x*4+y-2=y;

eq2:x+2=y;

eq3: pi*(1+(x-((a-1)/...

Calculate

gamma-integrate-solve

f(x, a, b):= (gamma(a...

solve(integrate(f(x, ...

Calculate

gamma-plot2d
plot2d([gamma(x),1/gamma(x)],[x,-4.5,5],[y,-10,10]);

plot2d([gamma(x),1/ga...

Calculate

gamma-inf-sum

sum(((gamma(k+3))*(su...

Calculate

gamma-integrate-log

f(s):=integrate((-log...

f(3);

f(2);

Calculate

gamma

Run Example
(%i1)eq1:x=lambda;
(%o1)                             x = lambda
(%i2) eq2:y=lambda+mu;
(%o2)                           y = lambda + mu
(%i3) eq3:z=gamma;
(%o3)                              z = gamma
(%i4) eq4:t=mu;
(%o4)                               t = mu
(%i5) ma:coefmatrix([eq1,eq2,eq3,eq4],[lambda,mu,gamma]);
                               [ - 1   0    0  ]
                               [               ]
                               [ - 1  - 1   0  ]
(%o5)                          [               ]
                               [  0    0   - 1 ]
                               [               ]
                               [  0   - 1   0  ]
(%i6) rank(ma);
(%o6)                                  3
(%i7) transpose(ma);
                            [ - 1  - 1   0    0  ]
                            [                    ]
(%o7)                       [  0   - 1   0   - 1 ]
                            [                    ]
                            [  0    0   - 1   0  ]
(%i8) newma:addcol(ma,[x,y,z,t]);
                             [ - 1   0    0   x ]
                             [                  ]
                             [ - 1  - 1   0   y ]
(%o8)                        [                  ]
                             [  0    0   - 1  z ]
                             [                  ]
                             [  0   - 1   0   t ]
(%i9) determinant:(ma);
                               [ - 1   0    0  ]
                               [               ]
                               [ - 1  - 1   0  ]
(%o9)                          [               ]
                               [  0    0   - 1 ]
                               [               ]
                               [  0   - 1   0  ]
(%i10) 
Run Example
diff(gamma(1+1/p),p);
                                 1            1
                            psi (- + 1) gamma(- + 1)
                               0 p            p
(%o1)                     - ------------------------
                                        2
                                       p
(%i2) diff(x^(1/p), p, inf);
                                  inf
                                 d       1/p
(%o2)                            ----- (x   )
                                   inf
                                 dp
(%i3) 
Run Example
r1: -3;
(%o1)                                 - 3
(%i2) r2: 4;
(%o2)                                  4
(%i3) f1_up:(-r1*r2*x+(r1-1)*(r2+1)^2);
(%o3)                             12 x - 100
(%i4) f1_down:(x-r2-1);
(%o4)                                x - 5
(%i5) f1 :f1_up/f1_down;
                                  12 x - 100
(%o5)                             ----------
                                    x - 5
(%i6) f2 : x^2-(r1-1)*x-(r1-1)*(r2+1);
                                  2
(%o6)                            x  + 4 x + 20
(%i7) pf1 : diff(f1, x);
                               12     12 x - 100
(%o7)                         ----- - ----------
                              x - 5           2
                                       (x - 5)
(%i8) pf2 : diff(f2, x);
(%o8)                               2 x + 4
(%i9) x1 : r1;
(%o9)                                 - 3
(%i10) x2 : r2;
(%o10)                                 4
(%i11) x0 : 0;
(%o11)                                 0
(%i12) fc1_1 : (ev(pf1, x=x1))*(x-x1)+ev(f1, x=x1);
                                5 (x + 3)
(%o12)                          --------- + 17
                                    8
(%i13) fc1_2 : (ev(pf1, x=x2))*(x-x2)+ev(f1, x=x2);
(%o13)                          40 (x - 4) + 52
(%i14) fc1_3 : (ev(pf1, x=x0))*(x-x0)+ev(f1, x=x0);
                                   8 x
(%o14)                             --- + 20
                                    5
(%i15) fc2_1 : (ev(pf2, x=x1))*(x-x1)+ev(f2, x=x1);
(%o15)                          17 - 2 (x + 3)
(%i16) fc2_2 : (ev(pf2, x=x2))*(x-x2)+ev(f2, x=x2);
(%o16)                          12 (x - 4) + 52
(%i17) fc2_3 : (ev(pf2, x=x0))*(x-x0)+ev(f2, x=x0);
(%o17)                             4 x + 20
(%i18) k1_1 : diff(fc1_1, x);
                                       5
(%o18)                                 -
                                       8
(%i19) k1_2 : diff(fc1_2, x);
(%o19)                                40
(%i20) k1_3 : diff(fc1_3, x);
                                       8
(%o20)                                 -
                                       5
(%i21) k2_1 : diff(fc2_1, x);
(%o21)                                - 2
(%i22) k2_2 : diff(fc2_2, x);
(%o22)                                12
(%i23) k2_3 : diff(fc2_3, x);
(%o23)                                 4
(%i24) alpha : atan(rat((k2_1 - k1_1)/(1 + k1_1*k2_1)));
                                        21
(%o24)                             atan(--)
                                        2
(%i25) beta : atan(rat((k2_2 - k1_2)/(1 + k1_2*k2_2)));
                                         28
(%o25)                            - atan(---)
                                         481
(%i26) gamma : atan(rat((k2_3 - k1_3)/(1 + k1_3*k2_3)));
                                        12
(%o26)                             atan(--)
                                        37
(%i27) 

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