this is for holding javascript data
Matt Pitkin added Expanding_out_alpha_we_get__.tex
over 8 years ago
Commit id: 1d4b1a126cf7d7d902aaed445f9397ceec95081b
deletions | additions
diff --git a/Expanding_out_alpha_we_get__.tex b/Expanding_out_alpha_we_get__.tex
new file mode 100644
index 0000000..8061237
--- /dev/null
+++ b/Expanding_out_alpha_we_get__.tex
...
Expanding out $\alpha$ we get
\begin{align}
\alpha =& a^{-1/3}\left(\frac{b^2}{3a} - \frac{2b^2}{3a} + c\right), \nonumber \\
=& a^{-1/3}\left(c - \frac{b^2}{3a}\right), \nonumber \\
=& \left(\frac{\pi}{3}\ddot{f_k}\right)^{-1/3} \pi \left(2(f_k-f) - \frac{\dot{f_k}^2}{\ddot{f_k}} \right) \label{eq:alpha}.
\end{align}
