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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.
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Transformation 1: given a product
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where are integers. Note, the code handles the case where , , and are GAMMA functions, and also the special case .
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Case 1: and . Then if , an integer, the product is multiplied by
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where is a correction factor depending on and .
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Similarly, CASE 2: where , . This is the case where the binomial appears in the denominator. Then if , an integer, the product is multiplied by
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Transformation 2: given a product
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where are integers and is a rational constant .
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Case 1: . Multiply by
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Case 2: . Multiply by
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