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{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:96%"
Table 68.  Computation of an Analytic Series in Symbolic Terms
+
|+ '''Table 68.  Computation of an Analytic Series in Symbolic Terms'''
o-----o-----o------------o----------o----------o----------o----------o----------o
+
|- style="background:paleturquoise"
| u v | f g |     Df    |   Dg    |   df    |   dg    |   rf    |   rf    |
+
| ''u''&nbsp;&nbsp;''v''
o-----o-----o------------o----------o----------o----------o----------o----------o
+
| ''f''&nbsp;&nbsp;''g''
|     |     |           |         |         |         |         |         |
+
| D''f''
| 0 0 | 0 1 | ((du)(dv)) | (du, dv) | (du, dv) | (du, dv) | du  dv  |    ()   |
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| D''g''
|     |     |            |          |          |          |          |          |
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| d''f''
| 0 1 | 1 0 | (du) dv  | (du, dv) |   dv    | (du, dv) | du  dv  |   ()   |
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| d''g''
|     |     |           |         |         |         |         |         |
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| d<sup>2</sup>''f''
| 1 0 | 1 0 |   du (dv) | (du, dv) |   du    | (du, dv) | du  dv  |   ()   |
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| d<sup>2</sup>''g''
|     |     |           |         |         |         |         |         |
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|-
| 1 1 | 1 1 |   du  dv  | (du, dv) |   ()   | (du, dv) | du  dv  |   ()   |
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|
|     |    |            |          |          |          |          |          |
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{| align="center" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
o-----o-----o------------o----------o----------o----------o----------o----------o
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| 0&nbsp;&nbsp;0
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{| align="center" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
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| ((d''u'')(d''v''))
 +
|-
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| (d''u'')&nbsp;d''v''&nbsp;
 +
|-
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| &nbsp;d''u''&nbsp;(d''v'')
 +
|-
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| d''u''&nbsp;&nbsp;d''v''
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|}
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|
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{| align="center" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
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| (d''u'', d''v'')
 +
|-
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| (d''u'', d''v'')
 +
|-
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| (d''u'', d''v'')
 +
|-
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| (d''u'', d''v'')
 +
|}
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|
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{| align="center" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
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| (d''u'', d''v'')
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|-
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| d''v''
 +
|-
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| d''u''
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|-
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| (&nbsp;)
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|}
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|
 +
{| align="center" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
 +
| (d''u'', d''v'')
 +
|-
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| (d''u'', d''v'')
 +
|-
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| (d''u'', d''v'')
 +
|-
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| (d''u'', d''v'')
 +
|}
 +
|
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{| align="center" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
 +
| d''u'' d''v''
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|-
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| d''u'' d''v''
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|-
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| d''u'' d''v''
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|-
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| d''u'' d''v''
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|}
 +
|
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{| align="center" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
 +
| (&nbsp;)
 +
|-
 +
| (&nbsp;)
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|-
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| (&nbsp;)
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|-
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| (&nbsp;)
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|}
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|}
 +
<br>
    
Figure&nbsp;69 gives a graphical picture of the difference map D''F''&nbsp;=&nbsp;‹D''f'',&nbsp;D''g''› for the transformation ''F''&nbsp;=&nbsp;‹''f'',&nbsp;''g''›&nbsp;=&nbsp;‹((''u'')(''v'')),&nbsp;((''u'',&nbsp;''v''))›.  This depicts the same information about D''f'' and D''g'' that was given in the corresponding rows of the computation summary in Tables&nbsp;66-i and 66-ii, excerpted here:
 
Figure&nbsp;69 gives a graphical picture of the difference map D''F''&nbsp;=&nbsp;‹D''f'',&nbsp;D''g''› for the transformation ''F''&nbsp;=&nbsp;‹''f'',&nbsp;''g''›&nbsp;=&nbsp;‹((''u'')(''v'')),&nbsp;((''u'',&nbsp;''v''))›.  This depicts the same information about D''f'' and D''g'' that was given in the corresponding rows of the computation summary in Tables&nbsp;66-i and 66-ii, excerpted here:
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