合流超几何函数的零点性质

Abstract

Abstract:

There have been many applications of confluent hypergeometric functions in quantum mechanics and statistics. Furthermore, many problems in mathematical physics can be solved with the help of the location of zeros of confluent hypergeometric functions. In this paper, we study the zero sets of the confluent hypergeometric function 1F₁(α;γ;z):=zⁿ, where α,γ,γ-α∉Z_{≤ 0}, and show that if {z_n}_n=1^∞ is the zero set of F(α;γ;z) with multiple zeros repeated and modulus in increasing order, then there exists a constant M > 0 such that|z_n|≥ M_n for all n ≥ 1.

Key words: Confluent hypergeometric functions, Jensen Formula, Entire function, Zerosequence

CLC Number:

O174

Lin Weichuan, Luo Xudan. On the Zeros of Confluent Hypergeometric Functions[J].Acta mathematica scientia,Series A, 2017, 37(5): 801-807.

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References

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