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Asymptotics of the zeros of degenerate hypergeometric functions

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Abstract

We find the asymptotics of the zeros of the degenerate hypergeometric function (the Kummer function) Φ(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 Φ.

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  1. Moscow State University, Russia

    A. M. Sedletskii

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  1. A. M. Sedletskii
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Correspondence to A. M. Sedletskii.

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Sedletskii, A.M. Asymptotics of the zeros of degenerate hypergeometric functions. Math Notes 82, 229–237 (2007). https://doi.org/10.1134/S0001434607070280

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  • DOI: https://doi.org/10.1134/S0001434607070280

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