论文标题
麦克唐纳功能的上限和渐近扩展以及Kontorovich-Lebedev积分的总结性
Upper bounds and asymptotic expansion for Macdonald's function and the summability of the Kontorovich-Lebedev integrals
论文作者
论文摘要
为MacDonald函数$ k_ {iτ}（x）$建立了均匀的上限和具有明显剩余项的渐近扩展。例如，可以应用结果来研究琼斯（Jones）意义上的Kontorovich-Lebedev积分的总和。也就是说，我们肯定地回答了一个问题（参见[6]），这些积分是否在弱的意义上融合了指数类型的整个功能。
Uniform upper bounds and the asymptotic expansion with an explicit remainder term are established for the Macdonald function $K_{iτ}(x)$. The results can be applied, for instance, to study the summability of the divergent Kontorovich-Lebedev integrals in the sense of Jones. Namely, we answer affirmatively a question (cf. [6]) whether these integrals converge for even entire functions of the exponential type in a weak sense.
