A new generalization of binomial coefficients |
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| Authors: | Michel Lassalle |
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| Affiliation: | 1. Centre National de la Recherche Scientifique, Institut Gaspard-Monge, Université de Marne-la-Vallée, 77454, Marne-la-Vallée Cedex, France
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| Abstract: | Let t be a fixed parameter and x some indeterminate. We give some properties of the generalized binomial coefficients $genfrac{langle }{rangle}{0pt}{}{x}{k}$ inductively defined by $k/x genfrac{langle}{rangle}{0pt}{}{x}{k}= tgenfrac{langle}{rangle}{0pt}{}{x-1}{k-1} +(1-t)genfrac{langle}{rangle}{0pt}{}{x-2}{k-2}$ . |
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