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[define,exp,imagpart,integrate,plot2d,subst]

Run Example
(%i1)mu:1.03;
(%o1)                                1.03
(%i2) x:10;
(%o2)                                 10
(%i3) T:1;
(%o3)                                  1
(%i4) define(F(s), exp(s*T)*(mu+s*x)/(s^2));
                                                   s
                                   (10 s + 1.03) %e
(%o4)                      F(s) := -----------------
                                           2
                                          s
(%i5) plot2d(imagpart(F(0.99+s*%i)),[s,-50,50]);
plotplot2d(imagpart(F(0.99+s*%i)),[s,-50,50]);int: integrate(F(s),s);
(%o6)    1.03 gamma_incomplete(- 1, - s) - 10 gamma_incomplete(0, - s)
(%i7) outcome: subst(0.99+%i*50,s,int)-subst(0.99-%i*50,s,int);
(%o7) 10 (898.9427688382168 %i - 1625.405190853055)
 - 1.03 (46.6532758200615 %i + 23.15652268225795)
 + 1.03 (23.15652268225795 - 46.6532758200615 %i)
 - 10 (- 898.9427688382168 %i - 1625.405190853055)
(%i8) 
Run Example
mu:1.03;
(%o1)                                1.03
(%i2) x:10;
(%o2)                                 10
(%i3) T:1;
(%o3)                                  1
(%i4) define(F(s), exp(s*T)*(mu+s*x)/(s^2));
                                                   s
                                   (10 s + 1.03) %e
(%o4)                      F(s) := -----------------
                                           2
                                          s
(%i5) plot2d(imagpart(F(0.99+s*%i)),[s,-50,50]);
plotplot2d(imagpart(F(0.99+s*%i)),[s,-50,50]);int: integrate(F(s),s);
(%o6)    1.03 gamma_incomplete(- 1, - s) - 10 gamma_incomplete(0, - s)
(%i7) outcome: (subst(0.99+%i*50,s,int)-subst(0.99-%i*50,s,int))*%i;
(%o7) %i (10 (898.9427688382168 %i - 1625.405190853055)
 - 1.03 (46.6532758200615 %i + 23.15652268225795)
 + 1.03 (23.15652268225795 - 46.6532758200615 %i)
 - 10 (- 898.9427688382168 %i - 1625.405190853055))
(%i8) 
Run Example
mu:0.03;
(%o1)                                0.03
(%i2) x:100;
(%o2)                                 100
(%i3) T:1;
(%o3)                                  1
(%i4) define(F(s), exp(s*T)*(mu+s*x)/(s^2));
                                                   s
                                  (100 s + 0.03) %e
(%o4)                     F(s) := ------------------
                                           2
                                          s
(%i5) int: integrate(F(s),s);
(%o5)   0.03 gamma_incomplete(- 1, - s) - 100 gamma_incomplete(0, - s)
(%i6) plot2d(imagpart(F(0.99+s*%i)),[s,-50,50]);
plotplot2d(imagpart(F(0.99+s*%i)),[s,-50,50]);define(outcome(r,c),(subst(r+%i*c,s,int)-subst(r+%i*c,s,int))/(2*%pi*%i));
(%o7)                        outcome(r, c) := 0.0
(%i8) outcome(2,100);
(%o8)                                 0.0
(%i9) (subst(2+%i*100,s,int)-subst(2-%i*100,s,int))/(2*%pi*%i);
(%o9) - (%i (100 gamma_incomplete(0, 100 %i - 2)
 - 100 gamma_incomplete(0, - 100 %i - 2)
 - 0.03 gamma_incomplete(- 1, 100 %i - 2)
 + 0.03 gamma_incomplete(- 1, - 100 %i - 2)))/(2 %pi)
(%i10) test: x+mu*T;
(%o10)                              100.03
(%i11) 
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