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Analytic structure of Schläfli function

Published online by Cambridge University Press:  22 January 2016

Kazuhiko Aomoto
Kazuhiko Aomoto*
Affiliation:
University of Tokyo
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In this note it is shown that Schläfli function can be simply expressed in terms of hyperlogarithmic functions, namely iterated integrals of forms with logarithmic poles in the sense of K. T. Chen (Theorem 1). It is also discussed the relation between Schläfli function and hypergeometric ones of Mellin-Sato type (Theorem 2). From a combinatorial point of view the structure of hyperlogarithmic functions seem very interesting just as the dilog log (so-called Abel-Rogers function) has played a crucial part in Gelfand-Gabriev-Losik’s formula of 1st Pontrjagin classes. See also [3].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 68 , November 1977 , pp. 1 - 16
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1977

References

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