%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}