Changes

update
Line 6,845: Line 6,845:  
<br>
 
<br>
   −
<font face="courier new">
+
{| align="center" border="1" cellpadding="20" cellspacing="0" style="text-align:left; width:90%"
{| align="center" border="1" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
+
|+ style="height:30px" | <math>\text{Table 66-i.} ~~ \text{Computation Summary for}~ f(u, v) = \texttt{((} u \texttt{)(} v \texttt{))}\!</math>
|+ '''Table 66-i. Computation Summary for ''f''‹''u'', ''v''› = ((''u'')(''v''))'''
   
|
 
|
{| align="left" border="0" cellpadding="1" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
+
<math>\begin{array}{c*{8}{l}}
| <math>\epsilon</math>''f''
+
\boldsymbol\varepsilon f
| = || ''uv''        || <math>\cdot</math> || 1
+
& = & u \!\cdot\! v \cdot 1
| + || ''u''(''v'')   || <math>\cdot</math> || 1
+
& + & u \texttt{(} v \texttt{)} \cdot 1
| + || (''u'')''v''  || <math>\cdot</math> || 1
+
& + & \texttt{(} u \texttt{)} v \cdot 1
| + || (''u'')(''v'') || <math>\cdot</math> || 0
+
& + & \texttt{(} u \texttt{)(} v \texttt{)} \cdot 0
|-
+
\\[6pt]
| E''f''
+
\mathrm{E}f
| = || ''uv''        || <math>\cdot</math> || (d''u'' d''v'')
+
& = & u \!\cdot\! v \cdot \texttt{(} \mathrm{d}u \cdot \mathrm{d}v \texttt{)}
| + || ''u''(''v'')   || <math>\cdot</math> || (d''u (d''v''))
+
& + & u \texttt{(} v \texttt{)} \cdot \texttt{(} \mathrm{d}u \texttt{(} \mathrm{d}v \texttt{))}
| + || (''u'')''v''  || <math>\cdot</math> || ((d''u'') d''v'')
+
& + & \texttt{(} u \texttt{)} v \cdot \texttt{((} \mathrm{d}u \texttt{)} \mathrm{d}v \texttt{)}
| + || (''u'')(''v'') || <math>\cdot</math> || ((d''u'')(d''v''))
+
& + & \texttt{(} u \texttt{)(} v \texttt{)} \cdot \texttt{((} \mathrm{d}u \texttt{)(} \mathrm{d}v \texttt{))}
|-
+
\\[6pt]
| D''f''
+
\mathrm{D}J
| = || ''uv''        || <math>\cdot</math> || d''u'' d''v''
+
& = & u \!\cdot\! v \cdot \mathrm{d}u \cdot \mathrm{d}v
| + || ''u''(''v'')   || <math>\cdot</math> || d''u'' (d''v'')
+
& + & u \texttt{(} v \texttt{)} \cdot \mathrm{d}u \texttt{(} \mathrm{d}v \texttt{)}
| + || (''u'')''v''  || <math>\cdot</math> || (d''u'') d''v''
+
& + & \texttt{(} u \texttt{)} v \cdot \texttt{(} \mathrm{d}u \texttt{)} \mathrm{d}v
| + || (''u'')(''v'') || <math>\cdot</math> || ((d''u'')(d''v''))
+
& + & \texttt{(} u \texttt{)(} v \texttt{)} \cdot \texttt{((} \mathrm{d}u \texttt{)(} \mathrm{d}v \texttt{))}
|-
+
\\[6pt]
| d''f''
+
\mathrm{d}J
| = || ''uv''        || <math>\cdot</math> || 0
+
& = & u \!\cdot\! v \cdot 0
| + || ''u''(''v'')   || <math>\cdot</math> || d''u''
+
& + & u \texttt{(} v \texttt{)} \cdot \mathrm{d}u
| + || (''u'')''v''  || <math>\cdot</math> || d''v''
+
& + & \texttt{(} u \texttt{)} v \cdot \mathrm{d}v
| + || (''u'')(''v'') || <math>\cdot</math> || (d''u'', d''v'')
+
& + & \texttt{(} u \texttt{)(} v \texttt{)} \cdot \texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
|-
+
\\[6pt]
| r''f''
+
\mathrm{r}J
| = || ''uv''        || <math>\cdot</math> || d''u'' d''v''
+
& = & u \!\cdot\! v \cdot \mathrm{d}u \cdot \mathrm{d}v
| + || ''u''(''v'')   || <math>\cdot</math> || d''u'' d''v''
+
& + & u \texttt{(} v \texttt{)} \cdot \mathrm{d}u \cdot \mathrm{d}v
| + || (''u'')''v''  || <math>\cdot</math> || d''u'' d''v''
+
& + & \texttt{(} u \texttt{)} v \cdot \mathrm{d}u \cdot \mathrm{d}v
| + || (''u'')(''v'') || <math>\cdot</math> || d''u'' d''v''
+
& + & \texttt{(} u \texttt{)(} v \texttt{)} \cdot \mathrm{d}u \cdot \mathrm{d}v
 +
\end{array}</math>
 
|}
 
|}
|}
  −
</font>
      
<br>
 
<br>
   −
<font face="courier new">
+
{| align="center" border="1" cellpadding="20" cellspacing="0" style="text-align:left; width:90%"
{| align="center" border="1" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
+
|+ style="height:30px" | <math>\text{Table 66-ii.} ~~ \text{Computation Summary for}~ g(u, v) = \texttt{((} u \texttt{,} v \texttt{))}\!</math>
|+ '''Table 66-ii. Computation Summary for g‹''u'', ''v''› = ((''u'', ''v''))'''
   
|
 
|
{| align="left" border="0" cellpadding="1" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
+
<math>\begin{array}{c*{8}{l}}
| <math>\epsilon</math>''g''
+
\boldsymbol\varepsilon g
| = || ''uv''        || <math>\cdot</math> || 1
+
& = & u \!\cdot\! v \cdot 1
| + || ''u''(''v'')   || <math>\cdot</math> || 0
+
& + & u \texttt{(} v \texttt{)} \cdot 0
| + || (''u'')''v''  || <math>\cdot</math> || 0
+
& + & \texttt{(} u \texttt{)} v \cdot 0
| + || (''u'')(''v'') || <math>\cdot</math> || 1
+
& + & \texttt{(} u \texttt{)(} v \texttt{)} \cdot 1
|-
+
\\[6pt]
| E''g''
+
\mathrm{E}f
| = || ''uv''        || <math>\cdot</math> || ((d''u'', d''v''))
+
& = & u \!\cdot\! v \cdot \texttt{((} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{))}
| + || ''u''(''v'')   || <math>\cdot</math> || (d''u'', d''v'')
+
& + & u \texttt{(} v \texttt{)} \cdot \texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
| + || (''u'')''v''  || <math>\cdot</math> || (d''u'', d''v'')
+
& + & \texttt{(} u \texttt{)} v \cdot \texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
| + || (''u'')(''v'') || <math>\cdot</math> || ((d''u'', d''v''))
+
& + & \texttt{(} u \texttt{)(} v \texttt{)} \cdot \texttt{((} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{))}
|-
+
\\[6pt]
| D''g''
+
\mathrm{D}J
| = || ''uv''        || <math>\cdot</math> || (d''u'', d''v'')
+
& = & u \!\cdot\! v \cdot \texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
| + || ''u''(''v'')   || <math>\cdot</math> || (d''u'', d''v'')
+
& + & u \texttt{(} v \texttt{)} \cdot \texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
| + || (''u'')''v''  || <math>\cdot</math> || (d''u'', d''v'')
+
& + & \texttt{(} u \texttt{)} v \cdot \texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
| + || (''u'')(''v'') || <math>\cdot</math> || (d''u'', d''v'')
+
& + & \texttt{(} u \texttt{)(} v \texttt{)} \cdot \texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
|-
+
\\[6pt]
| d''g''
+
\mathrm{d}J
| = || ''uv''        || <math>\cdot</math> || (d''u'', d''v'')
+
& = & u \!\cdot\! v \cdot \texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
| + || ''u''(''v'')   || <math>\cdot</math> || (d''u'', d''v'')
+
& + & u \texttt{(} v \texttt{)} \cdot \texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
| + || (''u'')''v''  || <math>\cdot</math> || (d''u'', d''v'')
+
& + & \texttt{(} u \texttt{)} v \cdot \texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
| + || (''u'')(''v'') || <math>\cdot</math> || (d''u'', d''v'')
+
& + & \texttt{(} u \texttt{)(} v \texttt{)} \cdot \texttt{(} \mathrm{d}u \texttt{,} \mathrm{d}v \texttt{)}
|-
+
\\[6pt]
| r''g''
+
\mathrm{r}J
| = || ''uv''        || <math>\cdot</math> || 0
+
& = & u \!\cdot\! v \cdot 0
| + || ''u''(''v'')   || <math>\cdot</math> || 0
+
& + & u \texttt{(} v \texttt{)} \cdot 0
| + || (''u'')''v''  || <math>\cdot</math> || 0
+
& + & \texttt{(} u \texttt{)} v \cdot 0
| + || (''u'')(''v'') || <math>\cdot</math> || 0
+
& + & \texttt{(} u \texttt{)(} v \texttt{)} \cdot 0
 +
\end{array}</math>
 
|}
 
|}
|}
  −
</font>
      
<br>
 
<br>
Line 6,929: Line 6,925:  
<br>
 
<br>
   −
{| align="center" border="1" cellpadding="0" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
+
{| align="center" border="1" cellpadding="0" cellspacing="0" style="font-weight:bold; text-align:center; width:90%"
 
|+ '''Table 67.  Computation of an Analytic Series in Terms of Coordinates'''
 
|+ '''Table 67.  Computation of an Analytic Series in Terms of Coordinates'''
 
|
 
|
Line 7,261: Line 7,257:  
<br>
 
<br>
   −
{| align="center" border="1" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:90%"
 
|+ '''Table 68.  Computation of an Analytic Series in Symbolic Terms'''
 
|+ '''Table 68.  Computation of an Analytic Series in Symbolic Terms'''
 
|- style="background:ghostwhite"
 
|- style="background:ghostwhite"
Line 7,362: Line 7,358:     
<font face="courier new">
 
<font face="courier new">
{| align="center" border="1" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:90%"
 
|
 
|
 
{| align="left" border="0" cellpadding="1" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
 
{| align="left" border="0" cellpadding="1" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
Line 7,401: Line 7,397:     
<font face="courier new">
 
<font face="courier new">
{| align="center" border="1" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:90%"
 
|
 
|
 
{| align="left" border="0" cellpadding="1" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
 
{| align="left" border="0" cellpadding="1" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
12,080

edits