Difference between revisions of "Jackson logarithm of a product"
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(Created page with "==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 $\lo...") |
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| + | *{{PaperReference|The time scale logarithm|2008|Billy Jackson|prev=Delta exponential of Jackson logarithm|next=findme}}: Theorem $1.2$, $(1.4)$ | ||
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 17:47, 11 February 2017
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.
Proof
References
- Billy Jackson: The time scale logarithm (2008)... (previous)... (next): Theorem $1.2$, $(1.4)$
