Analytic structure and explicit solution of an important implicit equation

R. Hagedorn, J. Rafelski

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


The equation z=2 G(z)-exp G(z)+1 (and similar ones obtained from it by substitutions) appears in connection with a variety of problems ranging from pure mathematics (combinatorics; some first order, nonlinear differential equations) over statistical thermodynamics to renormalization theory. It is therefore of interest to solve this equation for G(z) explicitly. It turns out, after study of the complex structure of the z and G planes, that an explicit integral representation of G(z) can be given, which may be directly used for numerical calculations of high precision.

Original languageEnglish (US)
Pages (from-to)563-578
Number of pages16
JournalCommunications in Mathematical Physics
Issue number4
StatePublished - Dec 1982

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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