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Diffstat (limited to 'info/mathtrip/src/ids3.tex')
-rw-r--r-- | info/mathtrip/src/ids3.tex | 25 |
1 files changed, 25 insertions, 0 deletions
diff --git a/info/mathtrip/src/ids3.tex b/info/mathtrip/src/ids3.tex new file mode 100644 index 0000000000..0a19c36a6c --- /dev/null +++ b/info/mathtrip/src/ids3.tex @@ -0,0 +1,25 @@ +%This command provides the text of the identities displayed at the +%top of page 3 +% +%The command has one parameter: +% 1) The width of the text +\newcommand\TTwoIdentities[1]{% + \parbox[t]{#1}{% + \TTwoFormulaeFontSize + \begin{DisplayFormulae}{38}{\SpaceBeforeFormula}{\TTwoInterlineFormulae}{\BigChar}{\StyleBold} + \Fm{\Cycle{n+1}{m+1} = \sum_k \Cycle{n}{k} \binom{k}{m} = \sum_{k=0}^n \Cycle{k}{m} + n^{\underline{n-k}} = n! \sum_{k=0}^n \frac{1}{k!} \Cycle{k}{m}} + \Fm{\Cycle{x}{x-n} = \sum_{k=0}^n \Euls{n}{k} \binom{x+k}{2n}} + \Fm{\SousEnsemble{n}{m} = \sum_k \binom{n}{k} \SousEnsemble{k+1}{m+1}(-1)^{n-k}} + \Fm{\Cycle{n}{m} = \sum_k \Cycle{n+1}{k+1} \binom{k}{m}(-1)^{m-k}} + \Fm{\SousEnsemble{m+n+1}{m} = \sum_{k=0}^m k \SousEnsemble{n+k}{k}} + \Fm{\Cycle{m+n+1}{m} = \sum_{k=0}^m k (n+k)\Cycle{n+k}{k}} + \Fm{\binom{n}{m} = \sum_k \SousEnsemble{n+1}{k+1} \Cycle{k}{m} (-1)^{m-k}} + \Fm{(n-m)!\binom{n}{m} = \sum_k \Cycle{n+1}{k+1} \SousEnsemble{k}{m} (-1)^{m-k}\MathRemark{\text{for }n \geq m}} + \Fm{\SousEnsemble{n}{n-m} = \sum_k \binom{m-n}{m+k} \binom{m+n}{n+k}\Cycle{m+k}{k}} + \Fm{\Cycle{n}{n-m} = \sum_k \binom{m-n}{m+k} \binom{m+n}{n+k}\SousEnsemble{m+k}{k}} + \Fm{\SousEnsemble{n}{\ell+m}\binom{\ell+m}{\ell} = \sum_k \SousEnsemble{k}{\ell} \SousEnsemble{n-k}{m} \binom{n}{k}} + \Fm{\Cycle{n}{\ell+m}\binom{\ell+m}{\ell} = \sum_k \Cycle{k}{\ell} \Cycle{n-k}{m} \binom{n}{k}} + \end{DisplayFormulae} + }% +} |