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Diffstat (limited to 'info/mathtrip/src/series2.tex')
-rw-r--r-- | info/mathtrip/src/series2.tex | 46 |
1 files changed, 46 insertions, 0 deletions
diff --git a/info/mathtrip/src/series2.tex b/info/mathtrip/src/series2.tex new file mode 100644 index 0000000000..5461f2a844 --- /dev/null +++ b/info/mathtrip/src/series2.tex @@ -0,0 +1,46 @@ +%The following command print all the series and their expansion +%which are typeset in the first horizontal part of the page 10. +% +%The macro has one parameter. +% 1) The width to use to typeset the formulae +% +\newcommand\TTenSerieTwo[1]{% + %This command typeset a line equation about the series on page 10 + % + %The command has 4 parameters + % 1) The first formula to be expanded + % 2) its expanded version + % 3) The second formula to be expanded + % 4) its expanded version + \def\LineOfArray##1##2##3##4{% + ##1&=&##2&##3&=&##4\\[\TTenExpansionSkip]% + }% + \parbox[t]{#1}{% + \TTenSeriesFontSize + \TTenTitle{Expansions:}% + $\displaystyle + \begin{array}{l@{\hspace{.1em}}c@{\hspace{.2em}}ll@{\hspace{.1em}}c@{\hspace{.2em}}l}% + \LineOfArray{\frac{1}{(1-x)^{n+1}}\ln\frac{1}{1- x}}% + {\sum_{i=0}^\infty (H_{n+i} - H_n) \binom{n+i}{i} x^i}% + {\left(\frac{1}{x}\right)^{\overline{-n}}}% + {\sum_{i=0}^\infty \SousEnsemble{i}{n} x^i}% + \LineOfArray{x^{\overline{n}}}% + {\sum_{i=0}^\infty \Cycle{n}{i} x^i}% + {(e^x - 1)^n}% + {\sum_{i=0}^\infty \SousEnsemble{i}{n} \frac{n! x^i}{i!}}% + \LineOfArray{\left(\ln \frac{1}{1 -x}\right)^n}% + {\sum_{i=0}^\infty \Cycle{i}{n} \frac{n! x^i}{i!}}% + {x \cot x}% + {\sum_{i=0}^\infty \frac{(-4)^i B_{2i} x^{2i}}{(2i)!}}% + \LineOfArray{\tan x}% + {\sum_{i=1}^\infty (-1)^{i-1}\frac{2^{2i} (2^{2i} - 1) B_{2i} x^{2i-1}}{(2i)!}}% + {\zeta(x)}% + {\sum_{i=1}^\infty \frac{1}{i^x}}% + \LineOfArray{\frac{1}{\zeta(x)}}% + {\sum_{i=1}^\infty \frac{\mu(i)}{i^x}}% + {\frac{\zeta(x-1)}{\zeta(x)}}% + {\sum_{i=1}^\infty \frac{\phi(i)}{i^x}}% + \end{array}$% + }% +} + |