Analytic structure and explicit solution of an important implicit equation

R. Hagedorn, Johann Rafelski

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

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
Volume83
Issue number4
DOIs
StatePublished - Dec 1982
Externally publishedYes

Fingerprint

Explicit Solution
Statistical Thermodynamics
Pure mathematics
mathematics
Combinatorics
Complex Structure
Renormalization
Integral Representation
Numerical Calculation
Nonlinear Differential Equations
Substitution
differential equations
substitutes
First-order
thermodynamics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

Analytic structure and explicit solution of an important implicit equation. / Hagedorn, R.; Rafelski, Johann.

In: Communications in Mathematical Physics, Vol. 83, No. 4, 12.1982, p. 563-578.

Research output: Contribution to journalArticle

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