## “School of Mathematics”

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Paper   IPM / M / 8304
School of Mathematics
Title:   Arithmetical properties of some series with logarithmic coefficient
Author(s):
 1 Kh. Hessami Pilehrood 2 T. Hessami Pilehrood
Status:   Published
Journal: Math. Z.
Vol.:  255
Year:  2007
Pages:   117-131
Supported by:  IPM
Abstract:
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.