Changes

MyWikiBiz, Author Your Legacy — Thursday May 02, 2024
Jump to navigationJump to search
update
Line 7,263: Line 7,263:  
<br>
 
<br>
   −
{| align="center" border="1" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:90%"
+
{| align="center" cellpadding="6" cellspacing="0" style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; text-align:center; width:90%"
|+ '''Table 68. Computation of an Analytic Series in Symbolic Terms'''
+
|+ style="height:30px" | <math>\text{Table 68.} ~~ \text{Computation of an Analytic Series in Symbolic Terms}\!</math>
|- style="background:ghostwhite"
+
|- style="height:35px; background:ghostwhite; width:100%"
| ''u''&nbsp;&nbsp;''v''
+
| <math>u\!</math>
| ''f''&nbsp;&nbsp;''g''
+
| <math>v\!</math>
| D''f''
+
| style="border-left:1px solid black" | <math>f\!</math>
| D''g''
+
| <math>g\!</math>
| d''f''
+
| style="border-left:1px solid black" | <math>{\mathrm{D}f}\!</math>
| d''g''
+
| <math>{\mathrm{D}g}\!</math>
| d<sup>2</sup>''f''
+
| style="border-left:1px solid black" | <math>{\mathrm{d}f}\!</math>
| d<sup>2</sup>''g''
+
| <math>{\mathrm{d}g}\!</math>
 +
| style="border-left:1px solid black" | <math>{\mathrm{d}^2\!f}\!</math>
 +
| <math>{\mathrm{d}^2\!g}\!</math>
 
|-
 
|-
|
+
| style="border-top:1px solid black" |
{| align="center" border="0" cellpadding="2" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
+
<math>\begin{matrix}
| 0&nbsp;&nbsp;0
+
0
|-
+
\\[4pt]
| 0&nbsp;&nbsp;1
+
0
|-
+
\\[4pt]
| 1&nbsp;&nbsp;0
+
1
|-
+
\\[4pt]
| 1&nbsp;&nbsp;1
+
1
|}
+
\end{matrix}</math>
|
+
| style="border-top:1px solid black" |
{| align="center" border="0" cellpadding="2" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
+
<math>\begin{matrix}
| 0&nbsp;&nbsp;1
+
0
|-
+
\\[4pt]
| 1&nbsp;&nbsp;0
+
1
|-
+
\\[4pt]
| 1&nbsp;&nbsp;0
+
0
|-
+
\\[4pt]
| 1&nbsp;&nbsp;1
+
1
|}
+
\end{matrix}</math>
|
+
| style="border-top:1px solid black; border-left:1px solid black" |
{| align="center" border="0" cellpadding="2" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
+
<math>\begin{matrix}
| ((d''u'')(d''v''))
+
0
|-
+
\\[4pt]
| (d''u'')&nbsp;d''v''&nbsp;
+
1
|-
+
\\[4pt]
| &nbsp;d''u''&nbsp;(d''v'')
+
1
|-
+
\\[4pt]
| d''u''&nbsp;&nbsp;d''v''
+
1
|}
+
\end{matrix}</math>
|
+
| style="border-top:1px solid black" |
{| align="center" border="0" cellpadding="2" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
+
<math>\begin{matrix}
| (d''u'', d''v'')
+
1
|-
+
\\[4pt]
| (d''u'', d''v'')
+
0
|-
+
\\[4pt]
| (d''u'', d''v'')
+
0
|-
+
\\[4pt]
| (d''u'', d''v'')
+
1
|}
+
\end{matrix}</math>
|
+
| style="border-top:1px solid black; border-left:1px solid black" |
{| align="center" border="0" cellpadding="2" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
+
<math>\begin{matrix}
| (d''u'', d''v'')
+
\texttt{((} \mathrm{d}u \texttt{)(} \mathrm{d}v \texttt{))}
|-
+
\\[4pt]
| d''v''
+
\texttt{~(} \mathrm{d}u \texttt{)~} \mathrm{d}v \texttt{~~}
|-
+
\\[4pt]
| d''u''
+
\texttt{~~} \mathrm{d}u \texttt{~(} \mathrm{d}v \texttt{)~}
|-
+
\\[4pt]
| (&nbsp;)
+
\texttt{~~} \mathrm{d}u \texttt{~~} \mathrm{d}v \texttt{~~}
|}
+
\end{matrix}</math>
|
+
| style="border-top:1px solid black" |
{| align="center" border="0" cellpadding="2" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
+
<math>\begin{matrix}
| (d''u'', d''v'')
+
\texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
|-
+
\\[4pt]
| (d''u'', d''v'')
+
\texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
|-
+
\\[4pt]
| (d''u'', d''v'')
+
\texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
|-
+
\\[4pt]
| (d''u'', d''v'')
+
\texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
|}
+
\end{matrix}</math>
|
+
| style="border-top:1px solid black; border-left:1px solid black" |
{| align="center" border="0" cellpadding="2" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
+
<math>\begin{matrix}
| d''u'' d''v''
+
\texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
|-
+
\\[4pt]
| d''u'' d''v''
+
\mathrm{d}v
|-
+
\\[4pt]
| d''u'' d''v''
+
\mathrm{d}u
|-
+
\\[4pt]
| d''u'' d''v''
+
0
|}
+
\end{matrix}</math>
|
+
| style="border-top:1px solid black" |
{| align="center" border="0" cellpadding="2" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
+
<math>\begin{matrix}
| (&nbsp;)
+
\texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
|-
+
\\[4pt]
| (&nbsp;)
+
\texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
|-
+
\\[4pt]
| (&nbsp;)
+
\texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
|-
+
\\[4pt]
| (&nbsp;)
+
\texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
|}
+
\end{matrix}</math>
 +
| style="border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}
 +
\mathrm{d}u \cdot \mathrm{d}v
 +
\\[4pt]
 +
\mathrm{d}u \cdot \mathrm{d}v
 +
\\[4pt]
 +
\mathrm{d}u \cdot \mathrm{d}v
 +
\\[4pt]
 +
\mathrm{d}u \cdot \mathrm{d}v
 +
\end{matrix}\!</math>
 +
| style="border-top:1px solid black" |
 +
<math>\begin{matrix}
 +
0
 +
\\[4pt]
 +
0
 +
\\[4pt]
 +
0
 +
\\[4pt]
 +
0
 +
\end{matrix}</math>
 
|}
 
|}
  
12,080

edits

Navigation menu