Let H be a hypergeometric term of n. The EfficientRepresentation[i](H,n) calling sequence constructs the ith efficient representation of H of the form  where alpha is a constant,  is a product of Gamma-function values and their reciprocals. Additionally,

 has the minimal number of factors,

 is a rational function which is minimal in one sense or another, depending on the particular rational canonical form chosen to represent the certificate of .

If  then  is minimal;

if  then  is minimal;

if  then  is minimal, and  is minimal;

if  then  is minimal, and  is minimal.

If EfficientRepresentation is called without an index, the first efficient representation is constructed.

Abramov, S.A.; Le, H.Q.; and Petkovsek, M. "Rational Canonical Forms and Efficient Representations of Hypergeometric Terms." Proc. ISSAC'2003, pp. 7-14. 2003.