Difference between revisions of "Bracket number"
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(Created page with "Define the bracket number operators (they are actually functions) $$[n]_{\mathbb{T}} = \left\{ \begin{array}{ll} 0 &; n=0 \\ [n-1]_{\mathbb{T}} \boxplus_{\mu} 1 &; n=1,2,\ldo...") |
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| − | + | Let $\mathbb{T}$ be a [[time scale]] and define the bracket numbers (they are actually functions) by | |
$$[n]_{\mathbb{T}} = \left\{ \begin{array}{ll} | $$[n]_{\mathbb{T}} = \left\{ \begin{array}{ll} | ||
0 &; n=0 \\ | 0 &; n=0 \\ | ||
[n-1]_{\mathbb{T}} \boxplus_{\mu} 1 &; n=1,2,\ldots | [n-1]_{\mathbb{T}} \boxplus_{\mu} 1 &; n=1,2,\ldots | ||
| − | \end{array} \right.$$ | + | \end{array} \right.,$$ |
| + | where $\boxplus$ denotes the [[forward box plus]] operation. | ||
| + | |||
| + | =Properties= | ||
| + | [[Gamma function on certain time scales at bracket number equals bracket factorial]] | ||
| + | |||
| + | =See also= | ||
| + | [[Gamma function]] | ||
| + | |||
| + | =References= | ||
| + | |||
| + | [[Category:Definition]] | ||
Latest revision as of 12:53, 16 January 2023
Let $\mathbb{T}$ be a time scale and define the bracket numbers (they are actually functions) by $$[n]_{\mathbb{T}} = \left\{ \begin{array}{ll} 0 &; n=0 \\ [n-1]_{\mathbb{T}} \boxplus_{\mu} 1 &; n=1,2,\ldots \end{array} \right.,$$ where $\boxplus$ denotes the forward box plus operation.
Properties
Gamma function on certain time scales at bracket number equals bracket factorial
