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Revision as of 21:48, 10 September 2013
, 21:48, 10 September 2013fix copy errors in old version of Table A6
Line 8,503:
Line 8,503:
| width="10%" |
| width="10%" |
| width="18%" | <math>f\!</math>
| width="18%" | <math>f\!</math>
−| width="18%" | <math>\mathrm{D}f|_{xy}</math>
+| width="18%" | <math>\mathrm{D}f|_{xy}\!</math>
−| width="18%" | <math>\mathrm{D}f|_{x(y)}</math>
+| width="18%" | <math>\mathrm{D}f|_{x(y)}\!</math>
−| width="18%" | <math>\mathrm{D}f|_{(x)y}</math>
+| width="18%" | <math>\mathrm{D}f|_{(x)y}~\!</math>
−| width="18%" | <math>\mathrm{D}f|_{(x)(y)}</math>
+| width="18%" | <math>\mathrm{D}f|_{(x)(y)}\!</math>
|-
|-
−| <math>f_0\!</math>
+| <math>f_{0}\!</math>
−| <math>(~)</math>
+| <math>(~)\!</math>
−| <math>(~)</math>
+| <math>(~)\!</math>
−| <math>(~)</math>
+| <math>(~)\!</math>
−| <math>(~)</math>
+| <math>(~)\!</math>
−| <math>(~)</math>
+| <math>(~)\!</math>
|-
|-
|
|
<math>\begin{matrix}
<math>\begin{matrix}
f_1
f_1
−\\[4pt]
+\\
f_2
f_2
−\\[4pt]
+\\
f_4
f_4
−\\[4pt]
+\\
f_8
f_8
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,528:
Line 8,528:
<math>\begin{matrix}
<math>\begin{matrix}
(x)(y)
(x)(y)
−\\[4pt]
+\\
(x)~y~
(x)~y~
−\\[4pt]
+\\
~x~(y)
~x~(y)
−\\[4pt]
+\\
~x~~y~
~x~~y~
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,538:
Line 8,538:
<math>\begin{matrix}
<math>\begin{matrix}
~~\mathrm{d}x~~\mathrm{d}y~~
~~\mathrm{d}x~~\mathrm{d}y~~
−\\[4pt]
+\\
~~\mathrm{d}x~(\mathrm{d}y)~
~~\mathrm{d}x~(\mathrm{d}y)~
−\\[4pt]
+\\
~(\mathrm{d}x)~\mathrm{d}y~~
~(\mathrm{d}x)~\mathrm{d}y~~
−\\[4pt]
+\\
((\mathrm{d}x)(\mathrm{d}y))
((\mathrm{d}x)(\mathrm{d}y))
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,548:
Line 8,548:
<math>\begin{matrix}
<math>\begin{matrix}
~~\mathrm{d}x~(\mathrm{d}y)~
~~\mathrm{d}x~(\mathrm{d}y)~
−\\[4pt]
+\\
~~\mathrm{d}x~~\mathrm{d}y~~
~~\mathrm{d}x~~\mathrm{d}y~~
−\\[4pt]
+\\
((\mathrm{d}x)(\mathrm{d}y))
((\mathrm{d}x)(\mathrm{d}y))
−\\[4pt]
+\\
~(\mathrm{d}x)~\mathrm{d}y~~
~(\mathrm{d}x)~\mathrm{d}y~~
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,558:
Line 8,558:
<math>\begin{matrix}
<math>\begin{matrix}
~(\mathrm{d}x)~\mathrm{d}y~~
~(\mathrm{d}x)~\mathrm{d}y~~
−\\[4pt]
+\\
((\mathrm{d}x)(\mathrm{d}y))
((\mathrm{d}x)(\mathrm{d}y))
−\\[4pt]
+\\
~~\mathrm{d}x~~\mathrm{d}y~~
~~\mathrm{d}x~~\mathrm{d}y~~
−\\[4pt]
+\\
~~\mathrm{d}x~(\mathrm{d}y)~
~~\mathrm{d}x~(\mathrm{d}y)~
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,568:
Line 8,568:
<math>\begin{matrix}
<math>\begin{matrix}
((\mathrm{d}x)(\mathrm{d}y))
((\mathrm{d}x)(\mathrm{d}y))
−\\[4pt]
+\\
~(\mathrm{d}x)~\mathrm{d}y~~
~(\mathrm{d}x)~\mathrm{d}y~~
−\\[4pt]
+\\
~~\mathrm{d}x~(\mathrm{d}y)~
~~\mathrm{d}x~(\mathrm{d}y)~
−\\[4pt]
+\\
~~\mathrm{d}x~~\mathrm{d}y~~
~~\mathrm{d}x~~\mathrm{d}y~~
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,579:
Line 8,579:
<math>\begin{matrix}
<math>\begin{matrix}
f_3
f_3
−\\[4pt]
+\\
f_{12}
f_{12}
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,585:
Line 8,585:
<math>\begin{matrix}
<math>\begin{matrix}
(x)
(x)
−\\[4pt]
+\\
~x~
~x~
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,591:
Line 8,591:
<math>\begin{matrix}
<math>\begin{matrix}
\mathrm{d}x
\mathrm{d}x
−\\[4pt]
+\\
\mathrm{d}x
\mathrm{d}x
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,597:
Line 8,597:
<math>\begin{matrix}
<math>\begin{matrix}
\mathrm{d}x
\mathrm{d}x
−\\[4pt]
+\\
\mathrm{d}x
\mathrm{d}x
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,603:
Line 8,603:
<math>\begin{matrix}
<math>\begin{matrix}
\mathrm{d}x
\mathrm{d}x
−\\[4pt]
+\\
\mathrm{d}x
\mathrm{d}x
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,609:
Line 8,609:
<math>\begin{matrix}
<math>\begin{matrix}
\mathrm{d}x
\mathrm{d}x
−\\[4pt]
+\\
\mathrm{d}x
\mathrm{d}x
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,616:
Line 8,616:
<math>\begin{matrix}
<math>\begin{matrix}
f_6
f_6
−\\[4pt]
+\\
f_9
f_9
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,622:
Line 8,622:
<math>\begin{matrix}
<math>\begin{matrix}
~(x,~y)~
~(x,~y)~
−\\[4pt]
+\\
((x,~y))
((x,~y))
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,628:
Line 8,628:
<math>\begin{matrix}
<math>\begin{matrix}
(\mathrm{d}x,~\mathrm{d}y)
(\mathrm{d}x,~\mathrm{d}y)
−\\[4pt]
+\\
(\mathrm{d}x,~\mathrm{d}y)
(\mathrm{d}x,~\mathrm{d}y)
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,634:
Line 8,634:
<math>\begin{matrix}
<math>\begin{matrix}
(\mathrm{d}x,~\mathrm{d}y)
(\mathrm{d}x,~\mathrm{d}y)
−\\[4pt]
+\\
(\mathrm{d}x,~\mathrm{d}y)
(\mathrm{d}x,~\mathrm{d}y)
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,640:
Line 8,640:
<math>\begin{matrix}
<math>\begin{matrix}
(\mathrm{d}x,~\mathrm{d}y)
(\mathrm{d}x,~\mathrm{d}y)
−\\[4pt]
+\\
(\mathrm{d}x,~\mathrm{d}y)
(\mathrm{d}x,~\mathrm{d}y)
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,646:
Line 8,646:
<math>\begin{matrix}
<math>\begin{matrix}
(\mathrm{d}x,~\mathrm{d}y)
(\mathrm{d}x,~\mathrm{d}y)
−\\[4pt]
+\\
(\mathrm{d}x,~\mathrm{d}y)
(\mathrm{d}x,~\mathrm{d}y)
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,653:
Line 8,653:
<math>\begin{matrix}
<math>\begin{matrix}
f_5
f_5
−\\[4pt]
+\\
f_{10}
f_{10}
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,659:
Line 8,659:
<math>\begin{matrix}
<math>\begin{matrix}
(y)
(y)
−\\[4pt]
+\\
~y~
~y~
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,665:
Line 8,665:
<math>\begin{matrix}
<math>\begin{matrix}
\mathrm{d}y
\mathrm{d}y
−\\[4pt]
+\\
\mathrm{d}y
\mathrm{d}y
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,671:
Line 8,671:
<math>\begin{matrix}
<math>\begin{matrix}
\mathrm{d}y
\mathrm{d}y
−\\[4pt]
+\\
\mathrm{d}y
\mathrm{d}y
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,677:
Line 8,677:
<math>\begin{matrix}
<math>\begin{matrix}
\mathrm{d}y
\mathrm{d}y
−\\[4pt]
+\\
\mathrm{d}y
\mathrm{d}y
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,683:
Line 8,683:
<math>\begin{matrix}
<math>\begin{matrix}
\mathrm{d}y
\mathrm{d}y
−\\[4pt]
+\\
\mathrm{d}y
\mathrm{d}y
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,690:
Line 8,690:
<math>\begin{matrix}
<math>\begin{matrix}
f_7
f_7
−\\[4pt]
+\\
f_{11}
f_{11}
−\\[4pt]
+\\
f_{13}
f_{13}
−\\[4pt]
+\\
f_{14}
f_{14}
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,700:
Line 8,700:
<math>\begin{matrix}
<math>\begin{matrix}
(~x~~y~)
(~x~~y~)
−\\[4pt]
+\\
(~x~(y))
(~x~(y))
−\\[4pt]
+\\
((x)~y~)
((x)~y~)
−\\[4pt]
+\\
((x)(y))
((x)(y))
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,710:
Line 8,710:
<math>\begin{matrix}
<math>\begin{matrix}
((\mathrm{d}x)(\mathrm{d}y))
((\mathrm{d}x)(\mathrm{d}y))
−\\[4pt]
+\\
~(\mathrm{d}x)~\mathrm{d}y~~
~(\mathrm{d}x)~\mathrm{d}y~~
−\\[4pt]
+\\
~~\mathrm{d}x~(\mathrm{d}y)~
~~\mathrm{d}x~(\mathrm{d}y)~
−\\[4pt]
+\\
~~\mathrm{d}x~~\mathrm{d}y~~
~~\mathrm{d}x~~\mathrm{d}y~~
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,720:
Line 8,720:
<math>\begin{matrix}
<math>\begin{matrix}
~(\mathrm{d}x)~\mathrm{d}y~~
~(\mathrm{d}x)~\mathrm{d}y~~
−\\[4pt]
+\\
((\mathrm{d}x)(\mathrm{d}y))
((\mathrm{d}x)(\mathrm{d}y))
−\\[4pt]
+\\
~~\mathrm{d}x~~\mathrm{d}y~~
~~\mathrm{d}x~~\mathrm{d}y~~
−\\[4pt]
+\\
~~\mathrm{d}x~(\mathrm{d}y)~
~~\mathrm{d}x~(\mathrm{d}y)~
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,730:
Line 8,730:
<math>\begin{matrix}
<math>\begin{matrix}
~~\mathrm{d}x~(\mathrm{d}y)~
~~\mathrm{d}x~(\mathrm{d}y)~
−\\[4pt]
+\\
~~\mathrm{d}x~~\mathrm{d}y~~
~~\mathrm{d}x~~\mathrm{d}y~~
−\\[4pt]
+\\
((\mathrm{d}x)(\mathrm{d}y))
((\mathrm{d}x)(\mathrm{d}y))
−\\[4pt]
+\\
~(\mathrm{d}x)~\mathrm{d}y~~
~(\mathrm{d}x)~\mathrm{d}y~~
\end{matrix}\!</math>
\end{matrix}\!</math>
Line 8,740:
Line 8,740:
<math>\begin{matrix}
<math>\begin{matrix}
~~\mathrm{d}x~~\mathrm{d}y~~
~~\mathrm{d}x~~\mathrm{d}y~~
−\\[4pt]
+\\
~~\mathrm{d}x~(\mathrm{d}y)~
~~\mathrm{d}x~(\mathrm{d}y)~
−\\[4pt]
+\\
~(\mathrm{d}x)~\mathrm{d}y~~
~(\mathrm{d}x)~\mathrm{d}y~~
−\\[4pt]
+\\
((\mathrm{d}x)(\mathrm{d}y))
((\mathrm{d}x)(\mathrm{d}y))
\end{matrix}\!</math>
\end{matrix}\!</math>
|-
|-
| <math>f_{15}\!</math>
| <math>f_{15}\!</math>
−| <math>((~))</math>
+| <math>((~))\!</math>
−| <math>((~))</math>
+| <math>(~)\!</math>
−| <math>((~))</math>
+| <math>(~)\!</math>
−| <math>((~))</math>
+| <math>(~)\!</math>
−| <math>((~))</math>
+| <math>(~)\!</math>
|}
|}
