Euler's factorial series and global relations

DOI10.1016/j.jnt.2017.09.026zbMath1444.11037arXiv1703.02633OpenAlexW2604791301MaRDI QIDQ1711699

Wadim Zudilin, Tapani Matala-aho

Publication date: 18 January 2019

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.02633

zbMATH Keywords

Padé approximationdivergent series\(p\)-adic

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Padé approximation (41A21) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Special functions in characteristic (p) (gamma functions, etc.) (33E50)

Related Items (13)

On Padé approximations and global relations of some Euler-type series ⋮ Arithmetic properties of the values of generalized hypergeometric series with polyadic transcendental parameters ⋮ Transcendence of \(p\)-adic values of generalized hypergeometric series with transcendental polyadic parameters ⋮ Irrationality of infinite series ⋮ Arithmetic properties of values at polyadic Liouville points of Euler-type series with polyadic Liouville parameter ⋮ Infinite linear independence with constraints on a subset of prime numbers for values of Euler-type series with polyadic Liouville parameter ⋮ Explicit results for Euler’s factorial series in arithmetic progressions under GRH ⋮ Euler's divergent series in arithmetic progressions ⋮ Arithmetic properties of Euler-type series with a Liouvillian polyadic parameter ⋮ New problems in the theory of transcendental polyadic numbers ⋮ Euler's factorial series at algebraic integer points ⋮ Product formula, global relations, and polyadic numbers ⋮ Euler's factorial series, Hardy integral, and continued fractions

Cites Work

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• Arithmetic properties of Euler series
• A determinantal approach to irrationality
• Type II Hermite-Padé approximations of generalized hypergeometric series
• On \(q\)-analogues of divergent and exponential series
• Euler's 1760 paper on divergent series
• Effective estimates for global relations on Euler-type series
• Euler’s constant: Euler’s work and modern developments
• Euler Subdues a Very Obstreperous Series

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