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Mat. Zametki, 2007, Volume 82, Issue 2, Pages 262–271 (Mi mz3787)  

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

Asymptotics of the Zeros of Degenerate Hypergeometric Functions

A. M. Sedletskii

M. V. Lomonosov Moscow State University

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

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

Full text: PDF file (488 kB)
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English version:
Mathematical Notes, 2007, 82:2, 229–237

Bibliographic databases:

UDC: 517.547.28
Received: 15.11.2005

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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Yukhimenko, “On a Class of Sine-Type Functions”, Math. Notes, 83:6 (2008), 858–870  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. A. Yu. Popov, A. M. Sedletskii, “Distribution of roots of Mittag-Leffler functions”, Journal of Mathematical Sciences, 190:2 (2013), 209–409  mathnet  crossref  mathscinet  zmath
    3. Sedletskii A.M., “Equivalence of the trigonometric system and its perturbations in L p(??,?)”, Dokl. Math., 94:1 (2016), 464–467  crossref  mathscinet  zmath  isi  elib  scopus
    4. 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  crossref  isi  elib  scopus
    5. 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  crossref  mathscinet  zmath  isi  scopus
    6. 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  mathnet  crossref  crossref  adsnasa  isi  elib
    7. Abuzyarova N.F., “Functions in the Schwartz Algebra That Are Invertible in the Sense of Ehrenpreis”, Dokl. Math., 99:1 (2019), 1–4  crossref  isi
    8. V. V. Kotlyar, A. A. Kovalev, E. G. Abramochkin, “Asimmetrichnye lazernye gipergeometricheskie puchki”, Kompyuternaya optika, 43:5 (2019), 735–740  mathnet  crossref
    9. 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  mathnet
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