M. G. Bashmakova, “Approximation of Values of the Gauss Hypergeometric Function by Rational Fractions”, Mat. Zametki, 88:6 (2010), 822–835; Math. Notes, 88:6 (2010), 785

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Matematicheskie Zametki, 2010, Volume 88, Issue 6, Pages 822–835
DOI: https://doi.org/10.4213/mzm8914 (Mi mzm8914)

This article is cited in 9 scientific papers (total in 9 papers)

Approximation of Values of the Gauss Hypergeometric Function by Rational Fractions

M. G. Bashmakova

Bryansk State Technical University

Full-text PDF (523 kB) Citations (9)

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DOI: https://doi.org/10.4213/mzm8914

Abstract: We consider a new approach to estimating the irrationality measure of numbers that are values of the Gauss hypergeometric function. Some of the previous results are improved, in particular, those concerning irrationalities of the form $\sqrt{k}\ln((\sqrt{k}+1)/(\sqrt{k}-1))$ with $k\in\mathbb N$.

Keywords: Gauss hypergeometric function, rational fraction, irrationality measure, Laplace method, Laurent series.

Received: 09.03.2010
Revised: 13.04.2010

English version:
Mathematical Notes, 2010, Volume 88, Issue 6, Pages 785–797
DOI: https://doi.org/10.1134/S0001434610110192

Bibliographic databases:

Document Type: Article

UDC: 511.36

Language: Russian

Citation: M. G. Bashmakova, “Approximation of Values of the Gauss Hypergeometric Function by Rational Fractions”, Mat. Zametki, 88:6 (2010), 822–835; Math. Notes, 88:6 (2010), 785–797

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm8914

https://doi.org/10.4213/mzm8914

https://www.mathnet.ru/eng/mzm/v88/i6/p822

This publication is cited in the following 9 articles:

M. G. Bashmakova, N. V. Sycheva, “O nekotorykh metodakh otsenki pokazatelya irratsionalnosti znachenii funktsii $\arctan x$”, Chebyshevskii sb., 25:1 (2024), 5–15
Mariya Bashmakova, Vladislav Salikhov, “Joint approximations of some values of the functions logx,arctanx”, Comb. Number Th., 13:3 (2024), 225
V. Kh. Salikhov, M. G. Bashmakova, “On irrationality measure of some values of $\arctan \frac{1}{n}$”, Russian Math. (Iz. VUZ), 64:12 (2020), 29–37
V. Kh. Salikhov, M. G. Bashmakova, “On irrationality measure $\mathrm{arctg}\, \frac {1}{3}$”, Russian Math. (Iz. VUZ), 63:1 (2019), 61–66
M. Yu. Luchin, V. Kh. Salikhov, E. S. Zolotukhina, “Ob otsenkakh lineinykh form ot logarifmov nekotorykh ratsionalnykh chisel”, Chebyshevskii sb., 20:4 (2019), 226–235
M. G. Bashmakova, V. Kh. Salikhov, “Ob otsenke mery irratsionalnosti $\mathop{\mathrm{arctg}}\frac12$”, Chebyshevskii sb., 20:4 (2019), 58–68
M. G. Bashmakova, E. S. Zolotukhina, “Ob otsenke mery irratsionalnosti chisel vida $\sqrt{4k+3}\ln{\frac{\sqrt{4k+3}+1}{\sqrt{4k+3}-1}}$ i $\frac{1}{\sqrt{k}}\mathrm{arctg}\,{\frac{1}{\sqrt{k}}}$”, Chebyshevskii sb., 19:2 (2018), 15–29
M. G. Bashmakova, E. S. Zolotukhina, “O pokazatelyakh irratsionalnosti chisel vida $\sqrt{d}\ln{\frac{\sqrt{d}+1}{\sqrt{d}-1}}$”, Chebyshevskii sb., 18:1 (2017), 29–43
Bashmakova M.G., “Dva podkhoda k otsenke mery irratsionalnosti znachenii gipergeometricheskoi funktsii s polutselymi parametrami”, Vestnik Bryanskogo gosudarstvennogo tekhnicheskogo universiteta, 2011, no. 2, 114–120

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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