Jackson logarithm of a product

Theorem

Let $\mathbb{T}$ be a time scale. The following formula holds: $$\log_{\mathbb{T}}(f(t)g(t))=\log_{\mathbb{T}} f(t) \oplus \log_{\mathbb{T}} g(t),$$ where $\log_{\mathbb{T}}$ denotes the Jackson logarithm and $\oplus$ denotes forward circle plus.

References

• Billy Jackson: The time scale logarithm (2008)... (previous)... (next): Theorem $1.2$, $(1.4)$