A. M. Sedletskii, “Asymptotics of the Zeros of Degenerate Hypergeometric Functions”, Mat. Zametki, 82:2 (2007), 262–271; Math. Notes, 82:2 (2007), 229

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Matematicheskie Zametki, 2007, Volume 82, Issue 2, Pages 262–271
DOI: https://doi.org/10.4213/mzm3787 (Mi mzm3787)

This article is cited in 16 scientific papers (total in 16 papers)

Asymptotics of the Zeros of Degenerate Hypergeometric Functions

A. M. Sedletskii

M. V. Lomonosov Moscow State University

Full-text PDF (488 kB) Citations (16)

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DOI: https://doi.org/10.4213/mzm3787

Abstract: We find the asymptotics of the zeros of the degenerate hypergeometric function (the Kummer function)

$\Phi(a,c;z)$ and indicate a method for numbering all of its zeros consistent with the asymptotics. This is done for the whole class of parameters

$a$ and

$c$ such that the set of zeros is infinite. As a corollary, we obtain the class of sine-type functions with unfamiliar asymptotics of their zeros. Also we prove a number of nonasymptotic properties of the zeros of the function

$\Phi$ .

Keywords: degenerate hypergeometric function (Kummer function), asymptotics of zeros, sine-type function, Kummer's formula, Laplace transform, entire function.

Received: 15.11.2005

English version:
Mathematical Notes, 2007, Volume 82, Issue 2, Pages 229–237
DOI: https://doi.org/10.1134/S0001434607070280

Bibliographic databases:

UDC: 517.547.28

Language: Russian

Citation: A. M. Sedletskii, “Asymptotics of the Zeros of Degenerate Hypergeometric Functions”, Mat. Zametki, 82:2 (2007), 262–271; Math. Notes, 82:2 (2007), 229–237

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Linking options:

https://www.mathnet.ru/eng/mzm3787

https://doi.org/10.4213/mzm3787

https://www.mathnet.ru/eng/mzm/v82/i2/p262

This publication is cited in the following 16 articles:

N. F. Abuzyarova, D. V. Semenova, “O delitelyakh v nekotorykh vesovykh algebrakh tselykh funktsii”, Vladikavk. matem. zhurn., 26:4 (2024), 5–20
N. F. Abuzyarova, “Perturbations of an Integer Sequence as Zero Sets of Divisors in Some Spaces of Entire Functions”, Math. Notes, 113:5 (2023), 613–623
N. F. Abuzyarova, Z. Yu. Fazullin, “On Properties of Zero Sets of Divisors in Weighted Spaces of Entire Functions”, Lobachevskii J Math, 44:6 (2023), 2192
V.V. Kotlyar, E.G. Abramochkin, A.A. Kovalev, A.G. Nalimov, “Astigmatic transformation of a fractional-order edge dislocation”, Computer Optics, 46:4 (2022)
Victor V Kotlyar, Eugeny G Abramochkin, Alexey A Kovalev, Anton G Nalimov, “An astigmatic transform of a fractional-order edge dislocation”, J. Opt., 24:6 (2022), 065602
Kotlyar V.V., Kovalev A.A., Abramochkin E.G., “Kummer Laser Beams With a Transverse Complex Shift”, J. Opt., 22:1 (2020), 015606
N. F. Abuzyarova, “On Shifts of the Sequence of Integers Generating Functions that are Invertible in the Sense of Ehrenpreis”, J Math Sci, 251:2 (2020), 161
A. M. Sedletskii, “Equivalence of the trigonometric system and its perturbations in the spaces $L^p$ and $C$ ”, Sb. Math., 210:4 (2019), 606–624
Abuzyarova N.F., “Functions in the Schwartz Algebra That Are Invertible in the Sense of Ehrenpreis”, Dokl. Math., 99:1 (2019), 1–4
V. V. Kotlyar, A. A. Kovalev, E. G. Abramochkin, “Asimmetrichnye lazernye gipergeometricheskie puchki”, Kompyuternaya optika, 43:5 (2019), 735–740
N. F. Abuzyarova, “O sdvigakh tselochislennoi posledovatelnosti, porozhdayuschikh funktsii, obratimye po Erenpraisu”, Issledovaniya po lineinym operatoram i teorii funktsii. 47, Zap. nauchn. sem. POMI, 480, POMI, SPb., 2019, 5–25
Abdulhameed M., Vieru D., Roslan R., Shafie S., “Analytical solution of convective oscillating flow at a sinusoidal pressure waveform”, Meccanica, 52:4-5 (2017), 941–954
Sedletskii A.M., “Equivalence of the trigonometric system and its perturbations in L p(??,?)”, Dokl. Math., 94:1 (2016), 464–467
Abdulhameed M., Roslan R., Bhadauria B.S., Hashim I., “Analytical Solution of Convective Heat Transfer of Oscillating Flow Subject to a Triangular Pressure Waveform”, Int. J. Fluid Mech. Res., 43:4 (2016), 333–349
A. Yu. Popov, A. M. Sedletskii, “Distribution of roots of Mittag-Leffler functions”, Journal of Mathematical Sciences, 190:2 (2013), 209–409
A. A. Yukhimenko, “On a Class of Sine-Type Functions”, Math. Notes, 83:6 (2008), 858–870

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

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