On the proximate order and lower proximate order for meromorphic functions

• Date: 2026
• Main Authors: Zabolotskyy, M., Zabolotskyy, T., Mostova, M., Заболоцький, Микола, Заболоцький, Тарас, Мостова, Мар'яна
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2026
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/9342
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For a function $\Gamma(r)=\exp\left\{\displaystyle\int\nolimits_1^r\dfrac{\gamma(t)}{t}dt\right\},$ $\gamma(r)$ is a proximate order, we deduce the expression $\Gamma(r)=r^{\gamma(r)}L(r),$ where $L(r)$ is a slowly varying function on $[1,+\infty),$ i.e., $rL'(r)/L(r)\to 0$ as $r\to+\infty....