The Ramanujan Journal

, Volume 14, Issue 1, pp 79–88 | Cite as

A generalization of an integral of Ramanujan



This paper considers a generalization of an integral introduced by S. Ramanujan in his third notebook. Ramanujan’s integral is itself a version of the dilogarithm,
$$Li_2(z) =-\int_{0}^{z}\frac{\log(1-x)}{x} \,\,dx.$$
We prove various functional equations and properties of the generalized integral.




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  1. 1.
    Berndt, B.C., Evans, R.J.: An integral functional equation of Ramanujan related to the dilogarithm. In: Mollin, R.A. (ed.) Number Theory de Gruyter pp. 1–5, Berlin, (1990)Google Scholar
  2. 2.
    Lewin, L.: Polylogarithms and Associated Functions. North-Holland, New York (1985)Google Scholar
  3. 3.
    Ramanujan, S.: Notebooks (2 vol.), Tata Institute of Fundamental Research, Bombay (1957)Google Scholar

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Syracuse UniversitySyracuseUSA

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