Q-difference equation for q-exponential E sub 1/q

Theorem

The following formula holds: $$D_q E_{\frac{1}{q}}(az)=aE_{\frac{1}{q}}(qaz),$$ where $D_q$ denotes the q-difference operator and $E_{\frac{1}{q}}$ denotes the $q$-exponential $E_{\frac{1}{q}}$.

References

• 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): ($6.154$)