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| <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'' ''v'' | + | | <math>u\!</math> |
− | | ''f'' ''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 0
| + | 0 |
− | |-
| + | \\[4pt] |
− | | 0 1
| + | 0 |
− | |-
| + | \\[4pt] |
− | | 1 0
| + | 1 |
− | |-
| + | \\[4pt] |
− | | 1 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 1
| + | 0 |
− | |-
| + | \\[4pt] |
− | | 1 0
| + | 1 |
− | |-
| + | \\[4pt] |
− | | 1 0
| + | 0 |
− | |-
| + | \\[4pt] |
− | | 1 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'') d''v''
| + | 1 |
− | |-
| + | \\[4pt] |
− | | d''u'' (d''v'')
| + | 1 |
− | |-
| + | \\[4pt] |
− | | d''u'' 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] |
− | | ( )
| + | \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} |
− | | ( )
| + | \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{)} |
− | |-
| + | \\[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> |
| + | | style="border-top:1px solid black" | |
| + | <math>\begin{matrix} |
| + | 0 |
| + | \\[4pt] |
| + | 0 |
| + | \\[4pt] |
| + | 0 |
| + | \\[4pt] |
| + | 0 |
| + | \end{matrix}</math> |
| |} | | |} |
| | | |