Difference between revisions of "Bracket factorial"
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(Created page with "Let $\mathbb{T}$ be a time scale. Define the bracket factorial by $$[n]_{\mathbb{T}}! = \left\{ \begin{array}{ll} 1&; n=0 \\ \displaystyle\prod_{j=1}^n [j]_{\mathbb{T}} &;...") |
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\end{array} \right.,$$ | \end{array} \right.,$$ | ||
where $[j]_{\mathbb{T}}$ denotes a [[bracket number]]. | where $[j]_{\mathbb{T}}$ denotes a [[bracket number]]. | ||
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| + | =Properties= | ||
| + | [[Gamma function on certain time scales at bracket number equals bracket factorial]] | ||
=See also= | =See also= | ||
Revision as of 18:08, 15 January 2023
Let $\mathbb{T}$ be a time scale. Define the bracket factorial by $$[n]_{\mathbb{T}}! = \left\{ \begin{array}{ll} 1&; n=0 \\ \displaystyle\prod_{j=1}^n [j]_{\mathbb{T}} &; n=1,2,\ldots \end{array} \right.,$$ where $[j]_{\mathbb{T}}$ denotes a bracket number.
Properties
Gamma function on certain time scales at bracket number equals bracket factorial
