Arithmetical properties of some series with logarithmic coefficients |
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Authors: | Khodabakhsh Hessami Pilehrood Tatiana Hessami Pilehrood |
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Institution: | (1) School of Mathematics, Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5746, Tehran, Iran;(2) Present address: Mathematics Department, Shahrekord University, P.O. Box 115, Shahrekord, Iran |
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Abstract: | We prove approximation formulas for the logarithms of some infinite products, in particular, for Euler’s constant γ, log
and log σ, where σ is 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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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 65B05 11J72 11Y60 |
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