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MyWikiBiz, Author Your Legacy — Thursday May 09, 2024
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"
|+ <math>\text{Table A3.}~~\operatorname{E}f ~\text{Expanded Over Differential Features}~ \{ \operatorname{d}x, \operatorname{d}y \}</math>
|+ <math>\text{Table A4.}~~\operatorname{D}f ~\text{Expanded Over Differential Features}~ \{ \operatorname{d}x, \operatorname{d}y \}</math>
|- style="background:#f0f0ff"
|- style="background:#f0f0ff"
| width="10%" |
| width="10%" |
| width="18%" | <math>f\!</math>
| width="18%" | <math>f\!</math>
| width="18%" |
| width="18%" |
<math>\operatorname{D}f|_{\operatorname{d}x~\operatorname{d}y}</math>
| width="18%" |
| width="18%" |
<math>\operatorname{D}f|_{\operatorname{d}x(\operatorname{d}y)}</math>
| width="18%" |
| width="18%" |
<math>\operatorname{D}f|_{(\operatorname{d}x)\operatorname{d}y}</math>
| width="18%" |
<math>\operatorname{D}f|_{(\operatorname{d}x)(\operatorname{d}y)}</math>
|-
|-
| <math>f_0\!</math>
| <math>f_0\!</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
((x,~y))
\\[4pt]
\\[4pt]
~x~(y)
~(x,~y)~
\\[4pt]
\\[4pt]
(x)~y~
~(x,~y)~
\\[4pt]
\\[4pt]
(x)(y)
((x,~y))
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
(y)
\\[4pt]
\\[4pt]
~y~
\\[4pt]
\\[4pt]
(y)
\\[4pt]
\\[4pt]
~y~
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
(x)~y~
(x)
\\[4pt]
\\[4pt]
(x)(y)
(x)
\\[4pt]
\\[4pt]
~x~~y~
~x~
\\[4pt]
\\[4pt]
~x~(y)
~x~
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
(x)(y)
(~)
\\[4pt]
\\[4pt]
(x)~y~
(~)
\\[4pt]
\\[4pt]
~x~(y)
(~)
\\[4pt]
\\[4pt]
~x~~y~
(~)
\end{matrix}</math>
\end{matrix}</math>
|-
|-
|
|
<math>\begin{matrix}
<math>\begin{matrix}
~x~
((~))
\\[4pt]
\\[4pt]
(x)
((~))
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
~x~
((~))
\\[4pt]
\\[4pt]
(x)
((~))
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
(x)
(~)
\\[4pt]
\\[4pt]
~x~
(~)
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
(x)
(~)
\\[4pt]
\\[4pt]
~x~
(~)
\end{matrix}</math>
\end{matrix}</math>
|-
|-
|
|
<math>\begin{matrix}
<math>\begin{matrix}
(~)
\\[4pt]
\\[4pt]
((x,~y))
(~)
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
((x,~y))
((~))
\\[4pt]
\\[4pt]
((~))
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
((x,~y))
((~))
\\[4pt]
\\[4pt]
((~))
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
(~)
\\[4pt]
\\[4pt]
((x,~y))
(~)
\end{matrix}</math>
\end{matrix}</math>
|-
|-
|
|
<math>\begin{matrix}
<math>\begin{matrix}
~y~
((~))
\\[4pt]
\\[4pt]
(y)
((~))
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
(y)
(~)
\\[4pt]
\\[4pt]
~y~
(~)
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
~y~
((~))
\\[4pt]
\\[4pt]
(y)
((~))
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
(y)
(~)
\\[4pt]
\\[4pt]
~y~
(~)
\end{matrix}</math>
\end{matrix}</math>
|-
|-
|
|
<math>\begin{matrix}
<math>\begin{matrix}
((x)(y))
((x,~y))
\\[4pt]
\\[4pt]
~(x,~y)~
\\[4pt]
\\[4pt]
~(x~(y))
~(x,~y)~
\\[4pt]
\\[4pt]
((x,~y))
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
~y~
\\[4pt]
\\[4pt]
(y)
\\[4pt]
\\[4pt]
~y~
\\[4pt]
\\[4pt]
(y)
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
~(x~(y))
~x~
\\[4pt]
\\[4pt]
~(x~~y)~
~x~
\\[4pt]
\\[4pt]
(x)
\\[4pt]
\\[4pt]
(x)
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
(~)
\\[4pt]
\\[4pt]
(~)
\\[4pt]
\\[4pt]
((x)~y)~
(~)
\\[4pt]
\\[4pt]
((x)(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>
|}
|}
