The Binomial Coefficient for Negative Arguments

Details The Binomial Coefficient for Negative Arguments The Binomial Coefficient for Negative Arguments

2011-05-18

arxiv.org/abs/1105.3689v1

Mathematics

Combinatorics

Scientific paper

The definition of the binomial coefficient in terms of gamma functions also allows non-integer arguments. For nonnegative integer arguments the gamma functions reduce to factorials, leading to the well-known Pascal triangle. Using a symmetry formula for the gamma function, this definition is extended to negative integer arguments, making it continuous at all integer arguments. The agreement of this definition with some other identities and with the binomial theorem is investigated.

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