Taiwanese Journal of Mathematics

NOTE ON THE IRRATIONALITY OF CERTAIN MULTIVARIATE $q$-FUNCTIONS

Peter Bundschuh

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Abstract

Various irrationality results on certain infinite series and products representing q-functions were established in recent years by Borwein, Lubinsky, and Zhou [1], [7-10]. In all these papers, Pad´e approximants to appropriate functions were constructed to produce rational approximations that are too rapid to be consistent with rationality. The main purpose of this note is to show how an old and seemingly forgotten irrationality criterion of the present author [3], particularly suited for q-functions, can be used to deduce very easily much more general results.

Article information

Source
Taiwanese J. Math., Volume 10, Number 3 (2006), 603-611.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500403849

Digital Object Identifier
doi:10.11650/twjm/1500403849

Mathematical Reviews number (MathSciNet)
MR2206316

Zentralblatt MATH identifier
1124.11034

Subjects
Primary: 11J72: Irrationality; linear independence over a field

Keywords
irrationality criterion Newton interpolation series $q$-functions

Citation

Bundschuh, Peter. NOTE ON THE IRRATIONALITY OF CERTAIN MULTIVARIATE $q$-FUNCTIONS. Taiwanese J. Math. 10 (2006), no. 3, 603--611. doi:10.11650/twjm/1500403849. https://projecteuclid.org/euclid.twjm/1500403849


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References

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