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Diffstat (limited to 'info/mathtrip/src/series4.tex')
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diff --git a/info/mathtrip/src/series4.tex b/info/mathtrip/src/series4.tex new file mode 100644 index 0000000000..26beaca666 --- /dev/null +++ b/info/mathtrip/src/series4.tex @@ -0,0 +1,50 @@ +%Produce the formulae in the first columns of the second horizontal +%part of page 10 +% +%The macrohas one parameter: +% 1) The size available to typeset the math +\newcommand\TTenSerieFour[1]{% + \parbox[t]{#1}{% + \TTenSeriesFontSize + %This command typeset a line equation about the series on page 10 + %when the serie is in one column + % + %The command has 2 parameters + % 1) The first formula to be expanded + % 2) its expanded version + \def\LineOfArray##1##2{% + ##1&=&##2\\[\TTenExpansionSkip]% + } + %To have some longer vertical space between some lines + %of the array (to better separate some equation). + \deflength\VSpace{1.2\TTenExpansionSkip} + $\displaystyle + \begin{array}{l@{\hspace{.1em}}c@{\hspace{.2em}}l} + \LineOfArray{\zeta(x)} + {\prod_p \frac{1}{1 - p^{-x}}} + \LineOfArray{\zeta^2(x)} + {\sum_{i=1}^\infty \frac{d(i)}{x^i}} + %The previous line is too long + & & \text{where }d(n) = \sum_{d \vert n} 1 \\[\VSpace] + \LineOfArray{\zeta(x)\zeta(x-1)} + {\sum_{i=1}^\infty \frac{S(i)}{x^i}} + %The previous line is too long + & & \text{where }S(n) = \sum_{d \vert n} d \\[\VSpace] + \LineOfArray{\zeta(2n)} + {\frac{2^{2n-1} \vert B_{2n} \vert}{(2n)!} \pi^{2n}, \quad n \in \Natural} + \LineOfArray{\frac{x}{\sin x}} + {\sum_{i=0}^\infty (-1)^{i-1}\frac{(4^i - 2) B_{2i} x^{2i}}{(2i)!}} + \LineOfArray{\left(\frac{1 - \sqrt{1-4x}}{2x}\right)^n} + {\sum_{i=0}^\infty \frac{n(2i + n - 1)!}{i! (n + i)!} x^i} + \LineOfArray{e^x \sin x}% + {\sum_{i=1}^\infty \frac{2^{i/2} \sin \tfrac{i \pi}{4}}{i!} x^i} + \LineOfArray{\frac{\sqrt{1 - \sqrt{1 -x}}}{x}}% + {\sum_{i=0}^\infty \frac{(4i)!}{16^i \sqrt{2} (2i)! (2i+1)!} x^i} + \LineOfArray{\left(\frac{\arcsin x}{x}\right)^2}% + {\sum_{i=0}^\infty \frac{ 4^i i!^2}{(i + 1)(2i +1)!} x^{2i}} + \end{array}$ + } +} +%The title of this part +%\newcommand\TTenSeriesBTitle{Series (continued)} +\newcommand\TTenSeriesBTitle{\relax} |