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Paper   IPM / M / 8304
School of Mathematics
  Title:   Arithmetical properties of some series with logarithmic coefficient
1.  Kh. Hessami Pilehrood
2.  T. Hessami Pilehrood
  Status:   Published
  Journal: Math. Z.
  Vol.:  255
  Year:  2007
  Pages:   117-131
  Supported by:  IPM
We prove that approximation formulas for the logarithms of some infinite products, in particular, for Euler's constant γ, log [4/(π)] and log σ, where σ in Somos's quadratic recurrence constant, in terms of classical Legendre polynomials and partial sums of their series expansions. We also give conditional irrationality and linear independence criteria for these numbers. The main tools are Euler-type integrals, hypergeometric series, and Laplace method.

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