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− | <font face="courier new">
| + | {| 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:70%" |
− | {| align="center" border="1" cellpadding="0" cellspacing="0" style="font-weight:bold; text-align:center; width:70%" | + | |+ style="height:30px" | <math>\text{Table 51.} ~~ \text{Computation of an Analytic Series in Symbolic Terms}\!</math> |
− | |+ Table 51. Computation of an Analytic Series in Symbolic Terms
| + | |- style="height:35px; background:ghostwhite; width:100%" |
− | |
| + | | <math>u\!</math> |
− | {| align="center" border="0" cellpadding="8" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:100%"
| + | | <math>v\!</math> |
− | | ''u'' || ''v'' | + | | style="border-left:1px solid black" | <math>J\!</math> |
− | |}
| + | | style="border-left:1px solid black" | <math>\mathrm{E}J\!</math> |
− | |
| + | | style="border-left:1px solid black" | <math>\mathrm{D}J\!</math> |
− | {| align="center" border="0" cellpadding="8" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:100%"
| + | | style="border-left:1px solid black" | <math>\mathrm{d}J\!</math> |
− | | ''J''
| + | | style="border-left:1px solid black" | <math>\mathrm{d}^2\!J\!</math> |
− | |} | |
− | |
| |
− | {| align="center" border="0" cellpadding="8" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:100%" | |
− | | E''J''
| |
− | |}
| |
− | | | |
− | {| align="center" border="0" cellpadding="8" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:100%"
| |
− | | D''J''
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− | |}
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− | |
| |
− | {| align="center" border="0" cellpadding="8" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:100%"
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− | | d''J'' | |
− | |} | |
− | | | |
− | {| align="center" border="0" cellpadding="8" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:100%"
| |
− | | d<sup>2</sup>''J'' | |
− | |} | |
− | |-
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− | |
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− | {| align="center" border="0" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
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− | | 0 || 0
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− | |-
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− | | 0 || 1
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− | |-
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− | | 1 || 0
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− | |-
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− | | 1 || 1
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− | |} | |
− | | | |
− | {| align="center" border="0" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
| |
− | | 0
| |
− | |-
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− | | 0
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− | |-
| |
− | | 0
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− | |-
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− | | 1
| |
− | |} | |
− | | | |
− | {| align="center" border="0" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
| |
− | | d''u'' d''v'' | |
− | |-
| |
− | | d''u'' (d''v'')
| |
− | |-
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− | | (d''u'') d''v''
| |
− | |-
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− | | (d''u'')(d''v'')
| |
− | |}
| |
− | | | |
− | {| align="center" border="0" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
| |
− | | d''u'' d''v'' | |
− | |-
| |
− | | d''u'' (d''v'')
| |
− | |-
| |
− | | (d''u'') d''v''
| |
− | |-
| |
− | | ((d''u'')(d''v''))
| |
− | |}
| |
− | |
| |
− | {| align="center" border="0" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:100%"
| |
− | | ()
| |
| |- | | |- |
− | | d''u'' | + | | style="border-top:1px solid black" | |
− | |- | + | <math>\begin{matrix} |
− | | d''v'' | + | 0 |
− | |-
| + | \\[4pt] |
− | | (d''u'', d''v'')
| + | 0 |
− | |}
| + | \\[4pt] |
− | |
| + | 1 |
− | {| align="center" border="0" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:100%" | + | \\[4pt] |
− | | d''u'' d''v''
| + | 1 |
− | |-
| + | \end{matrix}</math> |
− | | d''u'' d''v''
| + | | style="border-top:1px solid black" | |
− | |-
| + | <math>\begin{matrix} |
− | | d''u'' d''v''
| + | 0 |
− | |-
| + | \\[4pt] |
− | | d''u'' d''v''
| + | 1 |
− | |}
| + | \\[4pt] |
| + | 0 |
| + | \\[4pt] |
| + | 1 |
| + | \end{matrix}</math> |
| + | | style="border-top:1px solid black; border-left:1px solid black" | |
| + | <math>\begin{matrix} |
| + | 0 |
| + | \\[4pt] |
| + | 0 |
| + | \\[4pt] |
| + | 0 |
| + | \\[4pt] |
| + | 1 |
| + | \end{matrix}</math> |
| + | | style="border-top:1px solid black; border-left:1px solid black" | |
| + | <math>\begin{matrix} |
| + | \texttt{~} \mathrm{d}u \!\;\cdot\;\! \mathrm{d}v \texttt{~} |
| + | \\[4pt] |
| + | \texttt{~} \mathrm{d}u \texttt{~(} \mathrm{d}v \texttt{)} |
| + | \\[4pt] |
| + | \texttt{(} \mathrm{d}u \texttt{)~} \mathrm{d}v \texttt{~} |
| + | \\[4pt] |
| + | \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} |
| + | \texttt{~} \mathrm{d}u \!\;\cdot\;\! \mathrm{d}v \texttt{~} |
| + | \\[4pt] |
| + | \texttt{~} \mathrm{d}u \texttt{~(} \mathrm{d}v \texttt{)} |
| + | \\[4pt] |
| + | \texttt{(} \mathrm{d}u \texttt{)~} \mathrm{d}v \texttt{~} |
| + | \\[4pt] |
| + | \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} |
| + | 0 |
| + | \\[4pt] |
| + | \mathrm{d}u |
| + | \\[4pt] |
| + | \mathrm{d}v |
| + | \\[4pt] |
| + | \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> |
| |} | | |} |
− | </font>
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| <br> | | <br> |