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hgfred-load

load(orthopoly);

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

Calculate

hgfred

hgfred([1/2],[1], 5.7);

Calculate

hgfred

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

Calculate

hgfred-load

load(orthopoly);

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

Calculate

hgfred-load

load(orthopoly);

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

Calculate

hgfred-load

load(orthopoly);

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

Calculate

hgfred

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

Calculate

hgfred

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

Calculate

hgfred

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

Calculate

hgfred-load

load(orthopoly);

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

Calculate

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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