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The Ramanujan Journal

, Volume 34, Issue 1, pp 143–156 | Cite as

A new generalization of binomial coefficients

  • Michel Lassalle
Article

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 \(k/x \genfrac{\langle}{\rangle}{0pt}{}{x}{k}= t\genfrac{\langle}{\rangle}{0pt}{}{x-1}{k-1} +(1-t)\genfrac{\langle}{\rangle}{0pt}{}{x-2}{k-2}\).

Keywords

Generalized binomial coefficients 

Mathematics Subject Classification

05A10 11B65 

Notes

Acknowledgements

It is a pleasure to thank Christian Krattenthaler for a proof of Theorem 1.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Centre National de la Recherche Scientifique, Institut Gaspard-MongeUniversité de Marne-la-ValléeMarne-la-Vallée CedexFrance

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