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hgfred

hgfred([3/2,3/2],[5/2...

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hgfred

hgfred([1/2,1/2,1/2],...

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hgfred

hgfred([1/2,1/2],[1,3...

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hgfred

hgfred([1/2,1/2],[3/2...

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hgfred

hgfred([],[],x);

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hgfred

hgfred([1/2,1/2],[3/2...

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hgfred

hgfred([1/2,1/2],[3/2...

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hgfred

hgfred([1/2],[3/2,3/2...

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hgfred-load

load(orthopoly);

hgfred([-2],[a],z);

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hgfred

hgfred([1/2],[3/2,3/2...

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hgfred

Run Example
(%i1)hgfred([1/2],[3/2,3/2], 5.7);
                                   1    3  3
(%o1)                      %f    ([-], [-, -], 5.7)
                             1, 2  2    2  2
(%i2) 
Run Example
? hgfred;

 -- Function: hgfred (<a>, <b>, <t>)
     Simplify the generalized hypergeometric function in terms of other,
     simpler, forms.  <a> is a list of numerator parameters and <b> is
     a list of the denominator parameters.

     If `hgfred' cannot simplify the hypergeometric function, it returns
     an expression of the form `%f[p,q]([a], [b], x)' where <p> is the
     number of elements in <a>, and <q> is the number of elements in
     <b>.  This is the usual `pFq' generalized hypergeometric function.

          (%i1) assume(not(equal(z,0)));
          (%o1)                          [notequal(z, 0)]
          (%i2) hgfred([v+1/2],[2*v+1],2*%i*z);

                               v/2                               %i z
                              4    bessel_j(v, z) gamma(v + 1) %e
          (%o2)               ---------------------------------------
                                                 v
                                                z
          (%i3) hgfred([1,1],[2],z);

                                             log(1 - z)
          (%o3)                            - ----------
                                                 z
          (%i4) hgfred([a,a+1/2],[3/2],z^2);

                                         1 - 2 a          1 - 2 a
                                  (z + 1)        - (1 - z)
          (%o4)                   -------------------------------
                                           2 (1 - 2 a) z

     It can be beneficial to load orthopoly too as the following example
     shows.  Note that <L> is the generalized Laguerre polynomial.

          (%i5) load(orthopoly)$
          (%i6) hgfred([-2],[a],z);

                                              (a - 1)
                                           2 L       (z)
                                              2
          (%o6)                            -------------
                                             a (a + 1)
          (%i7) ev(%);

                                            2
                                           z        2 z
          (%o7)                         --------- - --- + 1
                                        a (a + 1)    a


(%o1)                                true
(%i2) 
Run Example
hgfred([5,6],[8], 5.7 - %i);
                         3    24 (2.931952807715581 %i + 1.569699811683202)
(%o1) - (7 (20 (%i - 4.7)  (- ---------------------------------------------
                                                         5
                                               (5.7 - %i)
             24                       12                         8
 - ---------------------- + ----------------------- - -----------------------
             4                        3           2             2           3
   (5.7 - %i)  (%i - 4.7)   (5.7 - %i)  (%i - 4.7)    (5.7 - %i)  (%i - 4.7)
             6                            4
 + ----------------------) - 10 (%i - 4.7)
                        4
   (5.7 - %i) (%i - 4.7)
  120 (2.931952807715581 %i + 1.569699811683202)            120
 (---------------------------------------------- + ----------------------
                             6                               5
                   (5.7 - %i)                      (5.7 - %i)  (%i - 4.7)
             60                        40                        30
 - ----------------------- + ----------------------- - -----------------------
             4           2             3           3             2           4
   (5.7 - %i)  (%i - 4.7)    (5.7 - %i)  (%i - 4.7)    (5.7 - %i)  (%i - 4.7)
             24                        5
 + ----------------------) + (%i - 4.7)
                        5
   (5.7 - %i) (%i - 4.7)
    720 (2.931952807715581 %i + 1.569699811683202)            720
 (- ---------------------------------------------- - ----------------------
                               7                               6
                     (5.7 - %i)                      (5.7 - %i)  (%i - 4.7)
             360                       240                       180
 + ----------------------- - ----------------------- + -----------------------
             5           2             4           3             3           4
   (5.7 - %i)  (%i - 4.7)    (5.7 - %i)  (%i - 4.7)    (5.7 - %i)  (%i - 4.7)
             144                      120                           3
 - ----------------------- + ----------------------)))/(8 (%i - 4.7) )
             2           5                        6
   (5.7 - %i)  (%i - 4.7)    (5.7 - %i) (%i - 4.7)
(%i2) 

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