doc/ratseries/slides/slide4.tex

   1 \magnification=\magstep3
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   6 \font\eins=cmb10 scaled \magstep 3
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   9 \def\frac#1#2{{{#1} \over {#2}}}
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  11 \vfill
  12
  13 \centerline{\eins Application to Euler's Constant}
  14 \bigskip\bigskip
  15 Put
  16 \quad\quad{$\displaystyle f(x) := {\sum\limits_{n=0}^{\infty} \frac{x^n}{{n!}^2}}$}\hfill\break
  17 \hphantom{Put}\quad\quad{$\displaystyle g(x) := {\sum\limits_{n=0}^{\infty} \left( \frac{1}{1} + \cdots + \frac{1}{n} \right) \frac{x^n}{{n!}^2}}$}\hfill\break
  18 \bigskip\bigskip
  19 Then
  20 \hfill{$\displaystyle \frac{g(x)}{f(x)} = \frac{1}{2} \log x + \gamma + O \left( e^{-4 \sqrt{x}} \right) $.}\hfill\break
  21 \bigskip\bigskip
  22 Choose $\displaystyle {x = {\left\lceil \frac{N \log 2}{4} \right\rceil}^2}$.
  23
  24 \vfill
  25 \hbox{}
  26 \eject
  27
  28 \end