Mathematica 4.2 Kernel for Power Macintosh
Copyright 1988-2002 Wolfram Research, Inc.
 -- Terminal graphics initialized -- 

In[1]:= 9^-27

                    1
Out[1]= --------------------------
        58149737003040059690390169

In[2]:= 12^144

Out[2]= 252405858452706802146088003199234910139421423537379794530169220964425\
 
>    944728647963794263559358200737721321118953128592183095980912780081856373\
 
>    786437365006336

In[3]:= Integrate[Sqrt[x]*Sqrt[a + x], x]

                                  3/2     2
                     a Sqrt[x]   x       a  Log[Sqrt[x] + Sqrt[a + x]]
Out[3]= Sqrt[a + x] (--------- + ----) - -----------------------------
                         4        2                    4

In[4]:= Solve[Sqrt[x] + a == 2*x, x]

               1 + 4 a - Sqrt[1 + 8 a]         1 + 4 a + Sqrt[1 + 8 a]
Out[4]= {{x -> -----------------------}, {x -> -----------------------}}
                          8                               8

In[5]:= Eigenvalues[{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}]

            3 (5 - Sqrt[33])  3 (5 + Sqrt[33])
Out[5]= {0, ----------------, ----------------}
                   2                 2

In[6]:= Sum[(j^m*Cos[(Pi*m)/4])/(m!^2*(m^2 + k)*(m^2 - l)), {m, 0, Infinity}]

Out[6]= (-((((-I Sqrt[k] (HypergeometricPFQ[{-Sqrt[l]}, {1, 1 - Sqrt[l]}, 
 
                        I j
>                     -------] / 2 + 
                       I/4 Pi
                      E
 
                                                                     I j
>                   HypergeometricPFQ[{Sqrt[l]}, {1, 1 + Sqrt[l]}, -------] / 
                                                                    I/4 Pi
                                                                   E
 
>                    2)) / (-I Sqrt[k] - Sqrt[l]) - 
 
>              (Sqrt[l] ((Sqrt[l] 
 
>                      HypergeometricPFQ[{I Sqrt[k]}, {1, 1 + I Sqrt[k]}, 
 
                          I j
>                       -------]) / (-I Sqrt[k] + Sqrt[l]) - 
                         I/4 Pi
                        E
 
>                   (I Sqrt[k] HypergeometricPFQ[{Sqrt[l]}, {1, 1 + Sqrt[l]}, 
 
                          I j
>                       -------]) / (-I Sqrt[k] + Sqrt[l]))) / 
                         I/4 Pi
                        E
 
>               (-I Sqrt[k] - Sqrt[l])) / 2 + 
 
>           ((I Sqrt[k] (HypergeometricPFQ[{-Sqrt[l]}, {1, 1 - Sqrt[l]}, 
 
                        I j
>                     -------] / 2 + 
                       I/4 Pi
                      E
 
                                                                     I j
>                   HypergeometricPFQ[{Sqrt[l]}, {1, 1 + Sqrt[l]}, -------] / 
                                                                    I/4 Pi
                                                                   E
 
>                    2)) / (I Sqrt[k] - Sqrt[l]) - 
 
>              (Sqrt[l] ((Sqrt[l] 
 
>                      HypergeometricPFQ[{-I Sqrt[k]}, {1, 1 - I Sqrt[k]}, 
 
                          I j
>                       -------]) / (I Sqrt[k] + Sqrt[l]) + 
                         I/4 Pi
                        E
 
>                   (I Sqrt[k] HypergeometricPFQ[{Sqrt[l]}, {1, 1 + Sqrt[l]}, 
 
                          I j
>                       -------]) / (I Sqrt[k] + Sqrt[l]))) / 
                         I/4 Pi
                        E
 
>               (I Sqrt[k] - Sqrt[l])) / 2) / (k l)) - 
 
>      (((-I Sqrt[k] (HypergeometricPFQ[{-Sqrt[l]}, {1, 1 - Sqrt[l]}, 
 
                       j
>                   -------] / 2 + 
                     I/4 Pi
                    E
 
                                                                    j
>                 HypergeometricPFQ[{Sqrt[l]}, {1, 1 + Sqrt[l]}, -------] / 2)
                                                                  I/4 Pi
                                                                 E
 
>               ) / (-I Sqrt[k] - Sqrt[l]) - 
 
>            (Sqrt[l] ((Sqrt[l] 
 
>                    HypergeometricPFQ[{I Sqrt[k]}, {1, 1 + I Sqrt[k]}, 
 
                         j
>                     -------]) / (-I Sqrt[k] + Sqrt[l]) - 
                       I/4 Pi
                      E
 
>                 (I Sqrt[k] HypergeometricPFQ[{Sqrt[l]}, {1, 1 + Sqrt[l]}, 
 
                         j
>                     -------]) / (-I Sqrt[k] + Sqrt[l]))) / 
                       I/4 Pi
                      E
 
>             (-I Sqrt[k] - Sqrt[l])) / 2 + 
 
>         ((I Sqrt[k] (HypergeometricPFQ[{-Sqrt[l]}, {1, 1 - Sqrt[l]}, 
 
                       j
>                   -------] / 2 + 
                     I/4 Pi
                    E
 
                                                                    j
>                 HypergeometricPFQ[{Sqrt[l]}, {1, 1 + Sqrt[l]}, -------] / 2)
                                                                  I/4 Pi
                                                                 E
 
>               ) / (I Sqrt[k] - Sqrt[l]) - 
 
>            (Sqrt[l] ((Sqrt[l] 
 
>                    HypergeometricPFQ[{-I Sqrt[k]}, {1, 1 - I Sqrt[k]}, 
 
                         j
>                     -------]) / (I Sqrt[k] + Sqrt[l]) + 
                       I/4 Pi
                      E
 
>                 (I Sqrt[k] HypergeometricPFQ[{Sqrt[l]}, {1, 1 + Sqrt[l]}, 
 
                         j
>                     -------]) / (I Sqrt[k] + Sqrt[l]))) / 
                       I/4 Pi
                      E
 
>             (I Sqrt[k] - Sqrt[l])) / 2) / (k l)) / 2

In[7]:= ParametricPlot3D[{u*Cos[u]*(4 + Cos[v + u]), u*Sin[u]*(4 + Cos[v + u]), u*Sin[v + u]}, {u, 0, 4*Pi}, {v, 0, 2*Pi}, PlotPoints -> {60, 12}]
                                                                              
                                                                              
                                                                              
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10######     #####****#####   ####**==#=##=#=########=#######=####   #######  
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-10####          ####%###############**##====#=##**##==####==######  ### 20   
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                                  25         #######    #### -40              
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Out[7]= -Graphics3D-

In[8]:=