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A hypergeometric approach, via linear forms involving logarithms, to criteria for irrationality of Euler's constant

In: Mathematica Slovaca, vol. 59, no. 3
Jonathan Sondow - Sergey Zlobin

Details:

Year, pages: 2009, 307 - 314
Keywords:
Euler’s constant, irrationality, hypergeometric, linear forms in logarithms
About article:
Using an integral of a hypergeometric function, we give necessary and sufficient conditions for irrationality of Euler's constant $γ$. The proof is by reduction to known irrationality criteria for $γ$ involving a Beukers-type double integral. We show that the hypergeometric and double integrals are equal by evaluating them. To do this, we introduce a construction of linear forms in $1$, $γ$, and logarithms from Nesterenko-type series of rational functions. In the Appendix, S. Zlobin gives a change-of-variables proof that the series and the double integral are equal.
How to cite:
ISO 690:
Sondow, J., Zlobin, S. 2009. A hypergeometric approach, via linear forms involving logarithms, to criteria for irrationality of Euler's constant. In Mathematica Slovaca, vol. 59, no.3, pp. 307-314. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0127-2

APA:
Sondow, J., Zlobin, S. (2009). A hypergeometric approach, via linear forms involving logarithms, to criteria for irrationality of Euler's constant. Mathematica Slovaca, 59(3), 307-314. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0127-2
About edition: