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The Maxima on-line user's manual

Algebra Calculator

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Hgfred Calculator

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.

hgfred([1/2],[3/2,3/2], 5.7);

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) 

Hgfred Example

Related Examples

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

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load(orthopoly);

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hgfred-load

load(orthopoly);

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

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

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