1/q-number as a q-number

Theorem

The following formula holds: $$[a]_{\frac{1}{q}}=q^{-a+1}[a]_q,$$ where $[a]_{\frac{1}{q}}$ denotes a $q$-number.

References

• 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): ($6.7$)