Mathematical Notes

, Volume 79, Issue 1–2, pp 97–108 | Cite as

On an Identity of Mahler

  • Yu. V. Nesterenko


We prove that certain multiple integrals depending on the complex parameter z can be expressed as polynomials in z and ln(1 − z). Similar identities were first used by K. Mahler in connection with the proofs of certain results of the theory of transcendental numbers.

Key words

Mahler's identity multiple integral transcendental numbers generalized polylogarithm Pade approximation Apery approximation Diophantine approximation 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Yu. V. Nesterenko
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityMoscowRussia

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