An Identity Involving the q-Factorial

Z. F. Koçak and G. M. Phillips

A chapter in Applications of Fibonacci Numbers, 1996, pp 291-296 from Springer

Abstract: Abstract Recently (see [4]) we have been studying B-splines when the intervals between consecutive knots are in geometric progression and, en passant, obtained the following identity: 1 $$ \left[ n \right]! = \sum\limits_{r = 0}^n {{{\left( { - 1} \right)}^{n - r}}{q^{ - \frac{1}{2}r\left( {2n - r - 1} \right)}}\left[ {\begin{array}{*{20}{c}} n \\ r \end{array}} \right]{{\left[ r \right]}^n}.} $$

Date: 1996
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DOI: 10.1007/978-94-009-0223-7_24

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