ISSAC 96 - Hypergeometric Function Representations Up
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Suitable Origins Previous Next

Can we compute ?  No.  Since applied to is

it would appear that

However, is undefined.  applied to would have the form

which is undefined.  Even worse, is false! At this equation gives

Referring back to their definitions, we see , , , and applied to are defined if , , and is distinct from all , and and is distinct from all , respectively.  Here,

Definition.  A pair is a suitable origin if
(1) and are free of nonpositive integers
(2) and are disjoint
(3) Integer elements of are
( and )

Definition.  A pair is accessible from a pair if there exists a proper sequence of shift and inverse shift operators , , , and such that


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