ISSAC 96 - Hypergeometric Function Representations Up
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Shift Operators Previous Next

We define shift operators and which apply to expressions where and are constant vectors.  Let be the operator for differentiation.  It can be checked that

Define the shift operators by

We see that applied to increments the th upper index of .  Similarly, define the shift operator by

It can be seen that applied to decrements the th lower index of .  Visibly,

where are unit vectors.  We need and for and to be defined.  Next

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