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Re: HypergeometricPFQ


Sam Finn writes:

>The evaluation rules for HypergeometricPFQ are messed up: 
>
>In[1]:= Integrate[1/(x^(7/3)(x^2+1.44^2)),{x,1,Infinity}]
>
>                                  5    8
>Out[1]= 0.3 HypergeometricPFQ[{1, -}, {-}, -2.0736]
>                                  3    3

Simply replacing the HypergeometricPFQ by Hypergeometric2F1 will do the
trick.  This can be done automatically (and should be :-)


%1 /. HypergeometricPFQ[num:{a__},den:{b__}, z_] :>
                Hypergeometric2F1[a, b, z]      /;
                        Length[num] == 2 && Length[den] == 1

0.139291

Alternatively, Mathematica can handle the more general symbolic case
without a problem:


Integrate[1/(x^(7/3) (x^2+a^2)),{x,1,Infinity}]

         2 1/3           2 1/3
 3     (a )    Log[1 + (a )   ]
---- + ------------------------ + 
   2                4
4 a              2 a
 
      2/3   2 1/3           2 1/3  -I/3 Pi
  (-1)    (a )    Log[1 - (a )    E       ]
  ----------------------------------------- + 
                       4
                    2 a
 
      4/3   2 1/3           2 1/3  I/3 Pi
  (-1)    (a )    Log[1 - (a )    E      ]
  ----------------------------------------
                       4
                    2 a


Substituting in your numerical value (and using Chop to remove the small
complex part) yields the same answer:


% /. a -> 1.44 // N // Chop


0.139291

>P.S. And also, will somebody please remind me why I even bother trying
>to make productive use of Mathematica?

Because it is a good system :-)

Cheers,
        
Paul C. Abbott
Department of Physics
University of Western Australia
Nedlands  6009






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