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Functional equations of iterated integrals with regular singularities

Published online by Cambridge University Press:  22 January 2016

Zdzisław Wojtkowiak
Zdzisław Wojtkowiak*
Affiliation:
Université de Nice-Sophia Antipolis Departement de Mathématiques, Laboratoire Jean Alexandre Dieudonné U.R.A. au C.N.R.S., No 168 Parc Valrose-B.P. N° 71 06108 Nice Cedex 2, France and Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa, Sakyo-ku, Kyoto 606, Japan
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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
Nagoya Mathematical Journal , Volume 142 , June 1996 , pp. 145 - 159
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1996

References

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[ 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