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declare

declare(j,imaginary);

eq3:V = E /(2*j*o*c*r...

eq2:o = %pi*2*f;

Calculate

declare-dotscrules-expand-limit-true

declare(a,scalar);

declare(T12, nonscala...

dotscrules:true;

Calculate

declare-ratsimp

declare([T1,T2,w], re...

ratsimp(T1^2*T2^2 - 2...

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declare-inf-limit

declare (n, integer);

a:(((4*n^2)+(5*n)-7)^...

limit(a,n,inf);

Calculate

declare-solve

eq: %e^(%i*x) = -1;

declare(x, real);

solve(eq);

Calculate

declare-solve-subst

eq1:x*9+y*5=1720;

declare(x, integerval...

declare(y, integerval...

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declare-solve-sqrt

declare( At, constant...

eq1: (L- v*t/sqrt(2))...

solve(eq1,t);

Calculate

declare-limit

declare(a,scalar);

declare(T12, nonscala...

I(X):=(X^^(-1));

Calculate

declare-is-rational

declare(v,rational);

is(1 = 1);

Calculate

declare

Run Example
(%i1)declare(k, integer);
(%o1)                                done
(%i2) declare(x, real);
(%o2)                                done
(%i3) is(%e^(%k) <
 %e^(%k*x^2));
(%o3)                               unknown
(%i4) 
Run Example
declare(m,integer);
(%o1)                                done
(%i2) factorial_expand:true;
(%o2)                                true
(%i3) epsilon(n,k):=(binomial(n,k)*gamma(3/2)/gamma(3/2-n+k)-(-1)^n*binomial(n-1,k-1)*n!/k!);
                                            3
                       binomial(n, k) gamma(-)
                                            2
(%o3) epsilon(n, k) := -----------------------
                                3
                          gamma(- - n + k)
                                2
                                                    n
                                               (- 1)  binomial(n - 1, k - 1) n!
                                             - --------------------------------
                                                              k!
(%i4) G(m):=-m*(4*m-3)/2;
                                    (- m) (4 m - 3)
(%o4)                       G(m) := ---------------
                                           2
(%i5) rat(epsilon(2*m,2*m-4)-G(m)*epsilon(2*m-1,2*m-4));
                8         7          6          5          4          3
(%o5)/R/ (1024 m  - 8704 m  + 30976 m  - 59680 m  + 67036 m  - 43756 m
                                                                 2
                                                        + 15309 m  - 2205 m)/96
(%i6) epsilon(4,1)-G(2)*epsilon(3,1);
                                      15
(%o6)                                 --
                                      4
(%i7) epsilon(2,1);
(%o7)                                 - 1
(%i8) epsilon(2,0);
                                        1
(%o8)                                 - -
                                        4
(%i9) 
Run Example
declare(S,real,Q,real, f,real,f0,real);
(%o1)                                done
(%i2) abs((S/(1 + %i*2*Q(f-f0)/f0))^2);
                                       2
                                      S
(%o2)                          ----------------
                                  2
                               4 Q (f - f0)
                               ------------ + 1
                                     2
                                   f0
(%i3) imagpart((S/(1 + %i*2*Q(f-f0)/f0)));
                                  2 Q(f - f0) S
(%o3)                       - ---------------------
                                  2
                               4 Q (f - f0)
                              (------------ + 1) f0
                                     2
                                   f0
(%i4) 
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