New irrationality measures for 𝑞-logarithms

DOI10.1090/S0025-5718-05-01812-0zbMath1158.11033MaRDI QIDQ3377000

Wadim Zudilin, Keijo Väänänen, Tapani Matala-aho

Publication date: 27 March 2006

Published in: Mathematics of Computation (Search for Journal in Brave)

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Measures of irrationality and of transcendence (11J82)

Related Items (7)

On the Dirichlet problem in rectangular domain for Lavrentiev-Bitsadze equation ⋮ On irrationality measures of \(\sum^{\infty}_{l=0}d^{l} / \prod^l_{j=1}(1+d^jr+d^{2j}s)\) ⋮ On the irrationality measure for certain series ⋮ On the irrationality of generalized \(q\)-logarithm ⋮ Leonhard Euler and a 𝑞-analogue of the logarithm ⋮ Irrationality proof of certain Lambert series using little \(q\)-Jacobi polynomials ⋮ Series and product representations for some mathematical constants

Cites Work

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• Remarks on irrationality of \(q\)-harmonic series
• Quantitative irrationality for sums of reciprocals of Fibonacci and Lucas numbers
• Little \(q\)-Legendre polynomials and irrationality of certain Lambert series.
• LCM of sequences of polynomials
• On the irrationality of \(\sum (1/(q^ n+r))\)
• Legendre type polynomials and irrationality measures.
• On approximation measures of q-logarithms
• Heine's basic transform and a permutation group for q-harmonic series

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