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Book:Leonard Lewin/Dilogarithms and Associated Functions - Revision history
2024-03-28T21:04:54Z
Revision history for this page on the wiki
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http://specialfunctionswiki.org/index.php?title=Book:Leonard_Lewin/Dilogarithms_and_Associated_Functions&diff=6973&oldid=prev
Tom at 20:56, 27 June 2016
2016-06-27T20:56:28Z
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 20:56, 27 June 2016</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:Chapter I The Dilogarithm</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:Chapter I The Dilogarithm</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::1. Introduction and Elementary Considerations</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::1. Introduction and Elementary Considerations</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:::[[Dilogarithm|(1.1)]]</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:::[[Dilogarithm|<ins class="diffchange diffchange-inline">$</ins>(1.1)<ins class="diffchange diffchange-inline">$]]</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:::[[Taylor series of log(1-z)|$(1.2)$</ins>]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::2. Extension to Large Real Values of $z$</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::2. Extension to Large Real Values of $z$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::3. Functional Equations Involving a Single Variable</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::3. Functional Equations Involving a Single Variable</div></td></tr>
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Tom
http://specialfunctionswiki.org/index.php?title=Book:Leonard_Lewin/Dilogarithms_and_Associated_Functions&diff=6967&oldid=prev
Tom at 20:49, 27 June 2016
2016-06-27T20:49:40Z
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 20:49, 27 June 2016</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l6" >Line 6:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:Chapter I The Dilogarithm</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>:Chapter I The Dilogarithm</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::1. Introduction and Elementary Considerations</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::1. Introduction and Elementary Considerations</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">:::[[Dilogarithm|(1.1)]]</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::2. Extension to Large Real Values of $z$</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::2. Extension to Large Real Values of $z$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::3. Functional Equations Involving a Single Variable</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::3. Functional Equations Involving a Single Variable</div></td></tr>
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Tom
http://specialfunctionswiki.org/index.php?title=Book:Leonard_Lewin/Dilogarithms_and_Associated_Functions&diff=6416&oldid=prev
Tom at 16:41, 21 June 2016
2016-06-21T16:41:11Z
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 16:41, 21 June 2016</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::6. Suggestions for Further Study</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::6. Suggestions for Further Study</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Category:<del class="diffchange diffchange-inline">Books</del>]]</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Category:<ins class="diffchange diffchange-inline">Book</ins>]]</div></td></tr>
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Tom
http://specialfunctionswiki.org/index.php?title=Book:Leonard_Lewin/Dilogarithms_and_Associated_Functions&diff=6297&oldid=prev
Tom at 16:38, 16 June 2016
2016-06-16T16:38:16Z
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 16:38, 16 June 2016</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td>
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<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{Book|<del class="diffchange diffchange-inline">Polylogarithms </del>and Associated Functions|<del class="diffchange diffchange-inline">1981</del>|<del class="diffchange diffchange-inline">North-Holland Publishing </del>Co.<del class="diffchange diffchange-inline">, New York-Amsterdam</del>||Leonard Lewin<del class="diffchange diffchange-inline">|ed = 2nd</del>}}</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{Book|<ins class="diffchange diffchange-inline">Dilogarithms </ins>and Associated Functions|<ins class="diffchange diffchange-inline">1958</ins>|<ins class="diffchange diffchange-inline">Macdonald & </ins>Co. <ins class="diffchange diffchange-inline">Ltd.</ins>||Leonard Lewin}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>===Contents===</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>===Contents===</div></td></tr>
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Tom
http://specialfunctionswiki.org/index.php?title=Book:Leonard_Lewin/Dilogarithms_and_Associated_Functions&diff=6296&oldid=prev
Tom at 16:36, 16 June 2016
2016-06-16T16:36:30Z
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 16:36, 16 June 2016</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l29" >Line 29:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::1. Introduction and Elementary Properties</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::1. Introduction and Elementary Properties</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::2. Differentiation with Respect to the Parameter</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::2. Differentiation with Respect to the Parameter</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::3. <del class="diffchange diffchange-inline">FOrmulae </del>Arising from a Change of Variable</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::3. <ins class="diffchange diffchange-inline">Formulae </ins>Arising from a Change of Variable</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::4. Formulae Arising from Inverse Tangent Integrals of Bi-Linear Argument</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::4. Formulae Arising from Inverse Tangent Integrals of Bi-Linear Argument</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::5. Formulae Arising from Inverse Tangent Integrals of Bi-Quadratic Argument</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::5. Formulae Arising from Inverse Tangent Integrals of Bi-Quadratic Argument</div></td></tr>
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Tom
http://specialfunctionswiki.org/index.php?title=Book:Leonard_Lewin/Dilogarithms_and_Associated_Functions&diff=6295&oldid=prev
Tom at 16:36, 16 June 2016
2016-06-16T16:36:17Z
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Tom
http://specialfunctionswiki.org/index.php?title=Book:Leonard_Lewin/Dilogarithms_and_Associated_Functions&diff=6237&oldid=prev
Tom at 06:34, 16 June 2016
2016-06-16T06:34:00Z
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::5. Bibliography</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::5. Bibliography</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::6. Suggestions for Further Study</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::6. Suggestions for Further Study</div></td></tr>
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</table>
Tom
http://specialfunctionswiki.org/index.php?title=Book:Leonard_Lewin/Dilogarithms_and_Associated_Functions&diff=6236&oldid=prev
Tom: Created page with "{{Book|Polylogarithms and Associated Functions|1981|North-Holland Publishing Co., New York-Amsterdam||Leonard Lewin|ed = 2nd}} ===Contents=== :Foreward :Preface :Chapter I Th..."
2016-06-16T06:33:48Z
<p>Created page with "{{Book|Polylogarithms and Associated Functions|1981|North-Holland Publishing Co., New York-Amsterdam||Leonard Lewin|ed = 2nd}} ===Contents=== :Foreward :Preface :Chapter I Th..."</p>
<p><b>New page</b></p><div>{{Book|Polylogarithms and Associated Functions|1981|North-Holland Publishing Co., New York-Amsterdam||Leonard Lewin|ed = 2nd}}<br />
<br />
===Contents===<br />
:Foreward<br />
:Preface<br />
:Chapter I The Dilogarithm<br />
::1. Introduction and Elementary Considerations<br />
::2. Extension to Large Real Values of $z$<br />
::3. Functional Equations Involving a Single Variable<br />
::4. Numerical Relations<br />
::5. Functional Relations Involving Two Variables<br />
::6. Newman's Functional Equation<br />
::7. Functional Equations Involving Several Variables<br />
::8. Legendre's Chi-function<br />
::9. Some Miscellaneous Results<br />
::10. A Survey of Definitions and Notations<br />
::11. Relations to Other Mathematical Functions<br />
::12. Occurrence in Physical Problems<br />
:Chapter II The Inverse Tangent Integral<br />
::1. Elementary Considerations and Definitions<br />
::2. The Inversion Relation<br />
::3. The Duplication Formula<br />
::4. Some Numerical Relations<br />
::5. The Triplication Formula<br />
::6. The Multiplication Formula for Odd Multiples<br />
::7. The Quadruplication Formula<br />
::8. Function Equations Involving Several Variables<br />
:Chapter III The Generalised Inverse Tangent Integral<br />
::1. Introduction and Elementary Properties<br />
::2. Differentiation with Respect to the Parameter<br />
::3. FOrmulae Arising from a Change of Variable<br />
::4. Formulae Arising from Inverse Tangent Integrals of Bi-Linear Argument<br />
::5. Formulae Arising from Inverse Tangent Integrals of Bi-Quadratic Argument<br />
::6. Factorisation Theorems<br />
::7. Multiplication Formulae<br />
::8. Derived Relations<br />
::9. Special Values of the Parameter<br />
::10. An Addition Equation Involving Argument and Parameter<br />
:Chapter IV Clausen's Integrals<br />
::1. Definition and Elementary Properties<br />
::2. Periodic Properties<br />
::3. The Factorisation Theorem<br />
::4. Series Expansions<br />
::5. Integral Relations<br />
::6. Functional Equations<br />
:Chapter V The Dilogarithm of Complex Argument<br />
::1. Resolution into Real and Imaginary Parts<br />
::2. The Factorisation Theorem<br />
::3. Special Values of the Argument<br />
::4. Functional Equations Involving a Single Variables<br />
::5. Defuction of $\mathrm{Li}_2(x,\theta)$ for Special Values of $\theta$<br />
::6. Newman's Functional Equation Involving Two Variables<br />
::7. Derived Functional Equations<br />
::8. Consequences of the Duplication Formula<br />
::9. An Addition Formula for the Angular Parameter<br />
:Chapter VI The Trilogarithm<br />
::1. Introduction and Elementary Considerations<br />
::2. Functional Equations of a Single Variable<br />
::3. Numerical Relations<br />
::4. A Consideration of Some Complex Forms<br />
::5. A Generalisation of Clausen's Integral<br />
::6. A Further Consideration of Complex Forms<br />
::7. Functional Equations of Two Variables<br />
::8. A Functional Equation of Newman's Type<br />
::9. Functional Equations Involving Several Variables<br />
:Chapter VII The Higher Order Functions<br />
::1. Introduction and Definitions<br />
::2. The Inversion Equation and Its Consequences<br />
::3. The Factorisation Theorem<br />
::4. Associated Integrals<br />
::5. The Associated Clausen Functions<br />
::6. Integral Relations for the Fourth Order Polylogarithm<br />
::7. Functional Equations for the Fourth Order Polylogarithm<br />
::8. Functional Equations for the Fifth Order Polylogarithm<br />
::9. The Log-Sine Integrals<br />
::10. Higher Order Polylogarithms<br />
:Chapter VIII The Integration of Functions and Summation of Series<br />
::1. The Reduction of a Class of Algebraic and Logarithmic Expressions<br />
::2. The Reduction of Trigonometric Forms<br />
::3. Summation of Series<br />
::4. Integrals from the Higher Order Functions<br />
:Chapter IX Reference Data and Tables<br />
::1. Glossary of Notation<br />
::2. List of Selected Formulae<br />
::3. Reference List of Integrals<br />
::4. Tabulated Values<br />
::5. Bibliography<br />
::6. Suggestions for Further Study</div>
Tom