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arXiv · 2211.08256

The q-Binomial Coefficient for Negative Arguments and Some q-Binomial Summation Identities

M. J. Kronenburg
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Abstract

Using a property of the q-shifted factorial, an identity for q-binomial coefficients is proved, which is used to derive the formulas for the q-binomial coefficient for negative arguments. The result is in agreement with an earlier paper about the normal binomial coefficient for negative arguments. Some new q-binomial summation identities are derived, and the formulas for negative arguments transform some of these summation identities into each other. One q-binomial summation identity is transformed into a new q-binomial summation identity.

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M. J. Kronenburg. 2023-01-11. The q-Binomial Coefficient for Negative Arguments and Some q-Binomial Summation Identities. https://arxiv.org/abs/2211.08256

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