Q-difference equation for q-exponential E sub q

Theorem

The following formula holds: $$D_q E_q(az) = aE_q(az),$$ where $D_q$ is the $q$-difference operator and $E_q$ is the $q$-exponential $E_q$.

References

• 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): ($6.152$)