Displaying similar documents to “On weighted densities”

Some remarks on I -faster convergent infinite series

Ladislav Matejíčka (2009)

Mathematica Bohemica

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A structure of terms of I -faster convergent series is studied in the paper. Necessary and sufficient conditions for the existence of I -faster convergent series with different types of their terms are proved. Some consequences are discussed.

A note on the transcendence of infinite products

Jaroslav Hančl, Ondřej Kolouch, Simona Pulcerová, Jan Štěpnička (2012)

Czechoslovak Mathematical Journal

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The paper deals with several criteria for the transcendence of infinite products of the form ∏ n = 1 ∞ [ b n α a n ] / b n α a n where α > 1 is a positive algebraic number having a conjugate α * such that α ≠ | α * | > 1 , { a n } n = 1 ∞ and { b n } n = 1 ∞ are two sequences of positive integers with some specific conditions. The proofs are based on the recent theorem of Corvaja and Zannier which relies on the Subspace Theorem (P. Corvaja, U. Zannier: On the rational approximation to the powers of an algebraic number: solution of two problems of Mahler and Mendès...