Journal of Mathematical Chemistry

, Volume 39, Issue 2, pp 259–266 | Cite as

Note on the Coulson integral formula

  • Ivan Gutman
  • Miodrag Mateljević


Let P be a polynomial of degree n, whose zeros λ1, λ2, ..., λ n are real-valued. The Coulson integral formula (first reported in 1940) is an expression for the sum of the positive–valued zeros of P, in terms of P. We show that the Coulson formula holds if and only if the condition λ12+...+λ n =0 is obeyed. We also show how the formula has to be modified, so that it be applicable in the case when λ12+...+λ n ≠ 0.


Coulson integral formula total π-electron energy HMO theory 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Faculty of ScienceUniversity of KragujevacKragujevacSerbia & Montenegro
  2. 2.Faculty of MathematicsUniversity of BelgradeBelgradeSerbia & Montenegro

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