Negation of binomial coefficients |
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Authors: | Renzo Sprugnoli |
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Institution: | aDipartimento di Sistemi e Informatica, Viale Morgagni, 65, 50134 Firenze, Italy |
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Abstract: | We extend the concept of a binomial coefficient to all integer values of its parameters. Our approach is purely algebraic, but we show that it is equivalent to the evaluation of binomial coefficients by means of the Γ-function. In particular, we prove that the traditional rule of “negation” is wrong and should be substituted by a slightly more complex rule. We also show that the “cross product” rule remains valid for the extended definition. |
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Keywords: | Binomial coefficients Negation of binomial coefficients Extended Pascal triangle |
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