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Diffstat (limited to 'info/mathtrip/src/ids2.tex')
-rw-r--r-- | info/mathtrip/src/ids2.tex | 38 |
1 files changed, 38 insertions, 0 deletions
diff --git a/info/mathtrip/src/ids2.tex b/info/mathtrip/src/ids2.tex new file mode 100644 index 0000000000..a7efbeac9f --- /dev/null +++ b/info/mathtrip/src/ids2.tex @@ -0,0 +1,38 @@ +%This command provides the identities in the third +%horizontal area in page 1 +%The macro has oe parameter: +% 1) The width of the text +\newcommand\TOneIdentitiesB[1]{% + \parbox[t]{#1}{% + \TOneFormulaeFontSize + \vspace{\TOnePushFormulaeB}% + \begin{DisplayFormulae}{19}{0pt}{\TOneInterlineFormulaeB}{\BigChar}{\StyleBold} + \Fm{\SousEnsemble{n}{n-1} = \Cycle{n}{n-1} = \binom{n}{2}} + \Fm{\sum_{k=0}^n\Cycle{n}{k} = n!} + \Fm{C_n = \frac{1}{n+1}\binom{2n}{n}} + \Fm{\Eul{n}{0} = \Eul{n}{n-1} = 1} + \Fm{\Eul{n}{k} = \Eul{n}{n-1-k}} + \Fm{\Eul{n}{k} = (k+1)\Eul{n-1}{k} + (n-k)\Eul{n-1}{k-1}} + \Fm{\Eul{0}{k} = \left\{% + \begin{array}{lr}% + 1 & \mbox{if }$k=0$, \\ + 0 & \mbox{otherwise} \\ + \end{array}% + \right.} + \Fm{\Eul{n}{1} = 2^n - n - 1} + \Fm{\Eul{n}{2} = 3^n - (n+1)2^n + \binom{n+1}{2}} + \Fm{x^n = \sum_{k=0}^n \Eul{n}{k} \binom{x+k}{n}} + \Fm{\Eul{n}{m} = \sum_{k=0}^m \binom{n+1}{k} (m+1-k)^n(-1)^k} + \Fm{m! \SousEnsemble{n}{m} = \sum_{k=0}^n \Eul{n}{k} \binom{k}{n-m}} + \Fm{\Eul{n}{m} =\sum_{k=0}^n \SousEnsemble{n}{k} \binom{n-k}{m} (-1)^{n-k-m}k!} + \Fm{\Euls{n}{0} = 1} + \Fm{\Euls{n}{n} = 0 \MathRemark{\text{for }n\neq 0}} + \Fm{\Euls{n}{k} = (k+1)\Euls{n-1}{k} + (2n-1-k)\Euls{n-1}{k-1}} + \Fm{\sum_{k=0}^n \Euls{n}{k} = \frac{(2n)^{\underline{n}}}{2^n}} + \Fm{\SousEnsemble{x}{x-n} = \sum_{k=0}^n \Euls{n}{k} \binom{x+n-1-k}{2n}} + \Fm{\SousEnsemble{n+1}{m+1} = \sum_k \binom{n}{k} \SousEnsemble{k}{m} = \sum_{k=0}^n \SousEnsemble{k}{m} (m+1)^{n-k}} + \end{DisplayFormulae} + %To keep a small horizontal white space after pushing the block + \vspace{1.1\TOnePushFormulaeB} + }% +} |