Geodesic
Asymptotics of the Zeros of Degenerate Hypergeometric Functions
Matematičeskie zametki, Tome 82 (2007) no. 2, pp. 262-271

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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, entire function.
Mots-clés : Laplace transform 
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     author = {A. M. Sedletskii},
     title = {Asymptotics of the {Zeros} of {Degenerate} {Hypergeometric} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {262--271},
     publisher = {mathdoc},
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     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_2_a10/}
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A. M. Sedletskii. Asymptotics of the Zeros of Degenerate Hypergeometric Functions. Matematičeskie zametki, Tome 82 (2007) no. 2, pp. 262-271. http://geodesic.mathdoc.fr/item/MZM_2007_82_2_a10/