- Title
- On the irrationality of generalized q-logarithm
- Creator
- Zudilin, Wadim
- Relation
- ARC
- Relation
- Research in Number Theory Vol. 2
- Publisher Link
- http://dx.doi.org/10.1007/s40993-016-0042-x
- Publisher
- SpringerOpen
- Resource Type
- journal article
- Date
- 2016
- Description
- For integer p, |p|>1, and generic rational x and z, we establish the irrationality of the series [formula could not be replicated].It is a symmetric (ℓp(x,z)=ℓp(z,x)) generalization of the q-logarithmic function (x = 1 and p = 1/q where |q|<1), which in turn generalizes the q-harmonic series (x = z = 1). Our proof makes use of the Hankel determinants built on the Padé approximations to ℓp(x,z).
- Subject
- irrationality; rational approximation; q-logarithm; q-harmonic series; basis hypergeometric series; Padé approximation; Hankel determinant
- Identifier
- http://hdl.handle.net/1959.13/1331570
- Identifier
- uon:26657
- Identifier
- ISSN:2363-9555
- Rights
- © 2016 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
- Language
- eng
- Full Text
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