This option to convert converts the GAMMA function and factorials in an expression e to binomial coefficients. The code performs the following two transformations on products of factorials and the GAMMA function.

Transformation 1: given a product

where  are integers. Note, the code handles the case where , , and  are GAMMA functions, and also the special case .

Case 1:  and .  Then if , an integer, the product is multiplied by

where  is a correction factor depending on  and .

Similarly, CASE 2: where , .  This is the case where the binomial appears in the denominator.  Then if , an integer, the product is multiplied by

Transformation 2: given a product

where  are integers and  is a rational constant .

Case 1: .  Multiply by   

Case 2: .  Multiply by