Abstract

Zeros of the modified Bessel function of the second kind (Macdonald function) \({{K}_{\nu }}\left( z \right)\) considered as a function of the index \(\nu \) are studied. It is proved that, for fixed \(z,\,z > 0\), the function \({{K}_{\nu }}\left( z \right)\) has a countable number of simple purely imaginary zeros \({{\nu }_{n}}\). The asymptotics of the zeros \({{\nu }_{n}}\) as \(n \to + \infty \) is found.

中文翻译：

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关于第二类修正贝塞尔函数的零点

摘要

第二类修正贝塞耳函数（麦克唐纳功能）的零点\（{{K} _ {\ NU}} \左（Z \右）\）视为指数的函数\（\ NU \）进行了研究。证明，对于固定的\（z，\，z> 0 \），函数\（{{K} _ {\ nu}} \ left（z \ right）\）具有可数的简单纯虚数零\（{{\ nu} _ {n}} \）。零点的渐近\（{{\ NU} _ {N}} \）作为\（N \至+ \ infty \）中找到。