  The incomplete beta function is an important special function in statistics.
In modern theory of hypergeometric functions, we regard hypergeometric
functions as pairings of twisted cycles and twisted cocycles. However, the
incomplete beta function cannot be understood in this scheme; in other words,
the domain of the integration is not cycle (incomplete). We will generalize the
theory of A-hypergeometric systems for incomplete functions. We give a general
study as well as a detailed study on an incomplete Gauss hypergeometric
function.
