Article contents
Functional equations of iterated integrals with regular singularities
Published online by Cambridge University Press: 22 January 2016
Extract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Polylogarithmic functions satisfy functional equations. The most famous equation is of course the functional equation of the logarithm
log x + log y = log(x · y).
The other well known equation is the Abel equation of the dilogarithm
- Type
- Research Article
- Information
- Copyright
- Copyright © Editorial Board of Nagoya Mathematical Journal 1996
References
[ 2 ]
Hill, C. J., Specimen exercitti analytici, functionum integralum
turn secundum amplitudinem, turn secundum modulum comparandi exhibentis, Lund, 9 (1830).Google Scholar
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20180130113655969-0203:S0027763000005675:S0027763000005675_inline2.gif?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20180130113655969-0203:S0027763000005675:S0027763000005675_inline3.gif?pub-status=live)
[ 3 ]
Hironaka, H., Resolution of singularities of an algebraic variety over a field of characteristic zero I II, Ann. of Math., 79 (1964) n° 1 and n° 2.Google Scholar
[ 4 ]
Lewin, L., The Evolution of the Ladder Concept, 1–10 in Structural Properties of Polylogarithms, Mathematical Surveys and Monographs, vol. 37, AMS, 1991.Google Scholar
[ 5 ]
Wojtkowiak, Z., The Basic Structure of Polylogarithmic Functional Equations, 205 — 231 in Structural Properties of Polylogarithms, L. Lewin, Editor, Mathematical Surveys and Monographs, vol. 37, AMS, 1991.Google Scholar
[ 6 ]
Magnus, W., Karrass, A. and Solitar, D., Combinatorial Group Theory, Pure and Applied Mathematics, XIII, Interscience Publ, 1966.Google Scholar
- 10
- Cited by