论文标题
拉普拉斯轮廓积分和线性微分方程
Laplace contour integrals and linear differential equations
论文作者
论文摘要
本文的目的是确定拉普拉斯轮廓积分的主要属性$$λ（z）= \ frac1 {2πi} \ int_ \ cccccart_l（t）e^{ - zt} \ $ l [w]（z）：= w^{（n）}+\ sum_ {j = 0}^{n-1}（a_j+b_jz）w^{（j）} = 0。溶液和相应的Nevanlinna功能。
The purpose of this paper is to determine the main properties of Laplace contour integrals $$Λ(z)=\frac1{2πi}\int_\CCϕ_L(t)e^{-zt}\,dt,$$ that solve linear differential equations $$L[w](z):=w^{(n)}+\sum_{j=0}^{n-1}(a_j+b_jz)w^{(j)}=0.$$ This concerns, in particular, the order of growth, asymptotic expansions, the Phragmén-Lindelöf indicator, the distribution of zeros, the existence of sub-normal and polynomial solutions, and the corresponding Nevanlinna functions.
