AperysConstant 2003-02-11 10:48:33 2003-10-22 21:58:59 Definition Riemann zeta function \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} \makeatletter \@ifundefined{bibname}{}{\renewcommand{\bibname}{References}} \makeatother The number \begin{align*} \zeta(3) &= \sum_{n=1}^\infty\frac{1}{n^3} \\ &= 1.202056903159594285399738161511449990764986292\ldots \end{align*} has been called Ap\'ery's constant since 1979, when Roger Ap\'ery published a remarkable proof that it is irrational \cite{cite:apery_irr}. \begin{thebibliography}{1} \bibitem{cite:apery_irr} Roger Ap{\'e}ry. \newblock Irrationalit{\'e} de $\zeta(2)$ et $\zeta(3)$. \newblock {\em Ast{\'e}risque}, 61:11--13, 1979. \bibitem{cite:poorten_aperyconst} Alfred van~der Poorten. \newblock A proof that {Euler} missed. {Ap{\'e}ry's} proof of the irrationality of $\zeta(3)$. An informal report. \newblock {\em Math. Intell.}, 1:195--203, 1979. \end{thebibliography} %@ARTICLE{cite:apery_irr, % author = {Roger Ap{\'e}ry}, % title = {Irrationalit{\'e} de $\zeta(2)$ et $\zeta(3)$}, % journal = {Ast{\'e}risque}, % volume = 61, % year = 1979, % pages = {11--13} %} % %@ARTICLE{cite:poorten_aperyconst, % author = {van der Poorten, Alfred}, % journal = {Math. Intell.}, % title = {A proof that {Euler} missed. {Ap{\'e}ry's} proof of the %irrationality of $\zeta(3)$. {An} informal report.}, % volume = 1, % year = 1979, % pages = {195--203} %}