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On Zeros of the Modified Bessel Function of the Second Kind
Computational Mathematics and Mathematical Physics ( IF 0.7 ) Pub Date : 2020-06-30 , DOI: 10.1134/s0965542520050048 S. M. Bagirova , A. Kh. Khanmamedov
中文翻译:
关于第二类修正贝塞尔函数的零点
更新日期:2020-06-30
Computational Mathematics and Mathematical Physics ( IF 0.7 ) Pub Date : 2020-06-30 , DOI: 10.1134/s0965542520050048 S. M. Bagirova , A. Kh. Khanmamedov
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:
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。